Journal articles: 'Weakly-coupled Oscillatory Neural Networks'

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Velichko, Andrey, Maksim Belyaev, Vadim Putrolaynen, Alexander Pergament, and Valentin Perminov. "Switching dynamics of single and coupled VO2-based oscillators as elements of neural networks." International Journal of Modern Physics B 31, no. 02 (January 18, 2017): 1650261. http://dx.doi.org/10.1142/s0217979216502611.

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In the present paper, we report on the switching dynamics of both single and coupled VO2-based oscillators, with resistive and capacitive coupling, and explore the capability of their application in oscillatory neural networks. Based on these results, we further select an adequate SPICE model to describe the modes of operation of coupled oscillator circuits. Physical mechanisms influencing the time of forward and reverse electrical switching, that determine the applicability limits of the proposed model, are identified. For the resistive coupling, it is shown that synchronization takes place at a certain value of the coupling resistance, though it is unstable and a synchronization failure occurs periodically. For the capacitive coupling, two synchronization modes, with weak and strong coupling, are found. The transition between these modes is accompanied by chaotic oscillations. A decrease in the width of the spectrum harmonics in the weak-coupling mode, and its increase in the strong-coupling one, is detected. The dependences of frequencies and phase differences of the coupled oscillatory circuits on the coupling capacitance are found. Examples of operation of coupled VO2 oscillators as a central pattern generator are demonstrated.

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Velichko, Andrei, Maksim Belyaev, and Petr Boriskov. "A Model of an Oscillatory Neural Network with Multilevel Neurons for Pattern Recognition and Computing." Electronics 8, no. 1 (January 9, 2019): 75. http://dx.doi.org/10.3390/electronics8010075.

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The current study uses a novel method of multilevel neurons and high order synchronization effects described by a family of special metrics, for pattern recognition in an oscillatory neural network (ONN). The output oscillator (neuron) of the network has multilevel variations in its synchronization value with the reference oscillator, and allows classification of an input pattern into a set of classes. The ONN model is implemented on thermally-coupled vanadium dioxide oscillators. The ONN is trained by the simulated annealing algorithm for selection of the network parameters. The results demonstrate that ONN is capable of classifying 512 visual patterns (as a cell array 3 × 3, distributed by symmetry into 102 classes) into a set of classes with a maximum number of elements up to fourteen. The classification capability of the network depends on the interior noise level and synchronization effectiveness parameter. The model allows for designing multilevel output cascades of neural networks with high net data throughput. The presented method can be applied in ONNs with various coupling mechanisms and oscillator topology.

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Aoyagi, Toshio, and Katsunori Kitano. "Retrieval Dynamics in Oscillator Neural Networks." Neural Computation 10, no. 6 (August 1, 1998): 1527–46. http://dx.doi.org/10.1162/089976698300017296.

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We present an analytical approach that allows us to treat the long-time behavior of the recalling process in an oscillator neural network. It is well known that in coupled oscillatory neuronal systems, under suitable conditions, the original dynamics can be reduced to a simpler phase dynamics. In this description, the phases of the oscillators can be regarded as the timings of the neuronal spikes. To attempt an analytical treatment of the recalling dynamics of such a system, we study a simplified model in which we discretize time and assume a synchronous updating rule. The theoretical results show that the retrieval dynamics is described by recursion equations for some macroscopic parameters, such as an overlap with the retrieval pattern. We then treat the noise components in the local field, which arise from the learning of the unretrieved patterns, as gaussian variables. However, we take account of the temporal correlation between these noise components at different times. In particular, we find that this correlation is essential for correctly predicting the behavior of the retrieval process in the case of autoassociative memory. From the derived equations, the maximal storage capacity and the basin of attraction are calculated and graphically displayed. We also consider the more general case that the network retrieves an ordered sequence of phase patterns. In both cases, the basin of attraction remains sufficiently wide to recall the memorized pattern from a noisy one, even near saturation. The validity of these theoretical results is supported by numerical simulations. We believe that this model serves as a convenient starting point for the theoretical study of retrieval dynamics in general oscillatory systems.

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KURRER, CHRISTIAN, and KLAUS SCHULTEN. "NEURONAL OSCILLATIONS AND STOCHASTIC LIMIT CYCLES." International Journal of Neural Systems 07, no. 04 (September 1996): 399–402. http://dx.doi.org/10.1142/s0129065796000373.

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We investigate a model for synchronous neural activity in networks of coupled neurons. The individual systems are governed by nonlinear dynamics and can continuously vary between excitable and oscillatory behavior. Analytical calculations and computer simulations show that coupled excitable systems can undergo two different phase transitions from synchronous to asynchronous firing behavior. One of the transitions is akin to the synchronization transitions in coupled oscillator systems, while the second transition can only be found in coupled excitable systems. Using the concept of Stochastic Limit Cycles, we present an analytical derivation of the two transitions and discuss implications for synchronization transitions in biological neural networks.

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Shahbazi, Hamed, Kamal Jamshidi, Amir Hasan Monadjemi, and Hafez Eslami Manoochehri. "Training oscillatory neural networks using natural gradient particle swarm optimization." Robotica 33, no. 7 (April 15, 2014): 1551–67. http://dx.doi.org/10.1017/s026357471400085x.

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SUMMARYIn this paper, a new design of neural networks is introduced, which is able to generate oscillatory patterns in its output. The oscillatory neural network is used in a biped robot to enable it to learn to walk. The fundamental building block of the neural network proposed in this paper is O-neurons, which can generate oscillations in its transfer functions. O-neurons are connected and coupled with each other in order to shape a network, and their unknown parameters are found by a particle swarm optimization method. The main contribution of this paper is the learning algorithm that can combine natural policy gradient with particle swarm optimization methods. The oscillatory neural network has six outputs that determine set points for proportional-integral-derivative controllers in 6-DOF humanoid robots. Our experiment on the simulated humanoid robot presents smooth and flexible walking.

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Jeong, Ho Young, and Boris Gutkin. "Synchrony of Neuronal Oscillations Controlled by GABAergic Reversal Potentials." Neural Computation 19, no. 3 (March 2007): 706–29. http://dx.doi.org/10.1162/neco.2007.19.3.706.

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GABAergic synapse reversal potential is controlled by the concentration of chloride. This concentration can change significantly during development and as a function of neuronal activity. Thus, GABA inhibition can be hyperpolarizing, shunting, or partially depolarizing. Previous results pinpointed the conditions under which hyperpolarizing inhibition (or depolarizing excitation) can lead to synchrony of neural oscillators. Here we examine the role of the GABAergic reversal potential in generation of synchronous oscillations in circuits of neural oscillators. Using weakly coupled oscillator analysis, we show when shunting and partially depolarizing inhibition can produce synchrony, asynchrony, and coexistence of the two. In particular, we show that this depends critically on such factors as the firing rate, the speed of the synapse, spike frequency adaptation, and, most important, the dynamics of spike generation (type I versus type II). We back up our analysis with simulations of small circuits of conductance-based neurons, as well as large-scale networks of neural oscillators. The simulation results are compatible with the analysis: for example, when bistability is predicted analytically, the large-scale network shows clustered states.

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Farokhniaee, AmirAli, Felix V. Almonte, Susanne Yelin, and Edward W. Large. "Entrainment of Weakly Coupled Canonical Oscillators with Applications in Gradient Frequency Neural Networks Using Approximating Analytical Methods." Mathematics 8, no. 8 (August 7, 2020): 1312. http://dx.doi.org/10.3390/math8081312.

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Solving phase equations for systems with high degrees of nonlinearities is cumbersome. However, in the case of two coupled canonical oscillators, that is, a reduced model of translated Wilson–Cowan neuronal dynamics, under slowly varying amplitude and rotating wave approximations, we suggested a convenient way to find their average relative phase evolution. This approach enabled us to find an explicit solution for the average relative phase of the two coupled canonical oscillators based on the original neuronal model parameters, and importantly, to find their phase-locking constraint. This methodology is straightforward to implement in any Wilson–Cowan-type coupled oscillators with applications in gradient frequency neural networks (GFNNs).

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Bathellier, Brice, Alan Carleton, and Wulfram Gerstner. "Gamma Oscillations in a Nonlinear Regime: A Minimal Model Approach Using Heterogeneous Integrate-and-Fire Networks." Neural Computation 20, no. 12 (December 2008): 2973–3002. http://dx.doi.org/10.1162/neco.2008.11-07-636.

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Fast oscillations and in particular gamma-band oscillation (20–80 Hz) are commonly observed during brain function and are at the center of several neural processing theories. In many cases, mathematical analysis of fast oscillations in neural networks has been focused on the transition between irregular and oscillatory firing viewed as an instability of the asynchronous activity. But in fact, brain slice experiments as well as detailed simulations of biological neural networks have produced a large corpus of results concerning the properties of fully developed oscillations that are far from this transition point. We propose here a mathematical approach to deal with nonlinear oscillations in a network of heterogeneous or noisy integrate-and-fire neurons connected by strong inhibition. This approach involves limited mathematical complexity and gives a good sense of the oscillation mechanism, making it an interesting tool to understand fast rhythmic activity in simulated or biological neural networks. A surprising result of our approach is that under some conditions, a change of the strength of inhibition only weakly influences the period of the oscillation. This is in contrast to standard theoretical and experimental models of interneuron network gamma oscillations (ING), where frequency tightly depends on inhibition strength, but it is similar to observations made in some in vitro preparations in the hippocampus and the olfactory bulb and in some detailed network models. This result is explained by the phenomenon of suppression that is known to occur in strongly coupled oscillating inhibitory networks but had not yet been related to the behavior of oscillation frequency.

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Zhang, Ting, Mohammad R. Haider, Yehia Massoud, and J. Iwan D. Alexander. "An Oscillatory Neural Network Based Local Processing Unit for Pattern Recognition Applications." Electronics 8, no. 1 (January 6, 2019): 64. http://dx.doi.org/10.3390/electronics8010064.

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Prolific growth of sensors and sensor technology has resulted various applications in sensing, monitoring, assessment and control operations. Owing to the large number of sensing units the the aggregate data volume creates a burden to the central data processing unit. This paper demonstrates an analog computational platform using weakly coupled oscillator neural network for pattern recognition applications. The oscillator neural network (ONN) has been studied over the last couple of decades for it’s increasing computational efficiency. The coupled ONN can realize the classification and pattern recognition functionalities based on its synchronization phenomenon. The convergence time and frequency of synchronization are considered as the indicator of recognition. For hierarchical sensing, the synchronization is detected in the first layer, and then the classification is accomplished in the second layer. In this work, a Kuramoto model based frequency synchronization approach is utilized, and simulation results indicate less than 160 ms convergence time and close frequency match for a simplified pattern recognition application. An array of 10 sensors is considered to affect the coupling weights of the oscillating nodes, and demonstrate network level computation. Based on MATLAB simulations, the proposed ONN architecture can successfully detect the close-in-match pattern through synchronization, and differentiate the far-out-match pattern through loss of synchronization in the oscillating nodes.

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Forrester, Michael, Jonathan J. Crofts, Stamatios N. Sotiropoulos, Stephen Coombes, and Reuben D. O’Dea. "The role of node dynamics in shaping emergent functional connectivity patterns in the brain." Network Neuroscience 4, no. 2 (January 2020): 467–83. http://dx.doi.org/10.1162/netn_a_00130.

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The contribution of structural connectivity to functional brain states remains poorly understood. We present a mathematical and computational study suited to assess the structure–function issue, treating a system of Jansen–Rit neural mass nodes with heterogeneous structural connections estimated from diffusion MRI data provided by the Human Connectome Project. Via direct simulations we determine the similarity of functional (inferred from correlated activity between nodes) and structural connectivity matrices under variation of the parameters controlling single-node dynamics, highlighting a nontrivial structure–function relationship in regimes that support limit cycle oscillations. To determine their relationship, we firstly calculate network instabilities giving rise to oscillations, and the so-called ‘false bifurcations’ (for which a significant qualitative change in the orbit is observed, without a change of stability) occurring beyond this onset. We highlight that functional connectivity (FC) is inherited robustly from structure when node dynamics are poised near a Hopf bifurcation, whilst near false bifurcations, and structure only weakly influences FC. Secondly, we develop a weakly coupled oscillator description to analyse oscillatory phase-locked states and, furthermore, show how the modular structure of FC matrices can be predicted via linear stability analysis. This study thereby emphasises the substantial role that local dynamics can have in shaping large-scale functional brain states.

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GÜZELIŞ, C. "CHAOTIC CELLULAR NEURAL NETWORKS MADE OF CHUA'S CIRCUITS." Journal of Circuits, Systems and Computers 03, no. 02 (June 1993): 603–12. http://dx.doi.org/10.1142/s021812669300037x.

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A chaotic neural network, called chaotic Cellular Neural Network (CNN), is proposed for performing complex information processing tasks. Each cell in the chaotic CNN is a Chua's circuit and connected only to its nearest neighbors. The proposed network of coupled Chua's circuit type cells constitutes a special case of the generalized CNNs introduced recently.1 Individual cells play the role of an analog microprocessor: producing constant, oscillatory or chaotic steady-state outputs depending on its input, which is the weighted sum of external inputs and the outputs of neighboring cells. The proposed chaotic CNN has complex temporal dynamical behaviours and hence provides a potentially rich mechanism for information processing, specially for nonlinear signal processing.

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Velichko, Andrei, Maksim Belyaev, Vadim Putrolaynen, and Petr Boriskov. "A New Method of the Pattern Storage and Recognition in Oscillatory Neural Networks Based on Resistive Switches." Electronics 7, no. 10 (October 22, 2018): 266. http://dx.doi.org/10.3390/electronics7100266.

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Development of neuromorphic systems based on new nanoelectronics materials and devices is of immediate interest for solving the problems of cognitive technology and cybernetics. Computational modeling of two- and three-oscillator schemes with thermally coupled VO2-switches is used to demonstrate a novel method of pattern storage and recognition in an impulse oscillator neural network (ONN), based on the high-order synchronization effect. The method allows storage of many patterns, and their number depends on the number of synchronous states Ns. The modeling demonstrates attainment of Ns of several orders both for a three-oscillator scheme Ns ~ 650 and for a two-oscillator scheme Ns ~ 260. A number of regularities are obtained, in particular, an optimal strength of oscillator coupling is revealed when Ns has a maximum. Algorithms of vector storage, network training, and test vector recognition are suggested, where the parameter of synchronization effectiveness is used as a degree of match. It is shown that, to reduce the ambiguity of recognition, the number coordinated in each vector should be at least one unit less than the number of oscillators. The demonstrated results are of a general character, and they may be applied in ONNs with various mechanisms and oscillator coupling topology.

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Reinhart, Robert M. G., and Geoffrey F. Woodman. "Oscillatory Coupling Reveals the Dynamic Reorganization of Large-scale Neural Networks as Cognitive Demands Change." Journal of Cognitive Neuroscience 26, no. 1 (January 2014): 175–88. http://dx.doi.org/10.1162/jocn_a_00470.

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Cognitive operations are thought to emerge from dynamic interactions between spatially distinct brain areas. Synchronization of oscillations has been proposed to regulate these interactions, but we do not know whether this large-scale synchronization can respond rapidly to changing cognitive demands. Here we show that, as task demands change during a trial, multiple distinct networks are dynamically formed and reformed via oscillatory synchronization. Distinct frequency-coupled networks were rapidly formed to process reward value, maintain information in visual working memory, and deploy visual attention. Strong single-trial correlations showed that networks formed even before the presentation of imperative stimuli could predict the strength of subsequent networks, as well as the speed and accuracy of behavioral responses seconds later. These frequency-coupled networks better predicted single-trial behavior than either local oscillations or ERPs. Our findings demonstrate the rapid reorganization of networks formed by dynamic activity in response to changing task demands within a trial.

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Cadieu, Charles F., and Kilian Koepsell. "Phase Coupling Estimation from Multivariate Phase Statistics." Neural Computation 22, no. 12 (December 2010): 3107–26. http://dx.doi.org/10.1162/neco_a_00048.

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Coupled oscillators are prevalent throughout the physical world. Dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real-world systems and are compelling models of neural systems. However, these formulations usually deal with the forward problem: simulating a system from known coupling parameters. Here we provide a solution to the inverse problem: determining the coupling parameters from measurements. Starting from the dynamic equations of a system of symmetrically coupled phase oscillators, given by a nonlinear Langevin equation, we derive the corresponding equilibrium distribution. This formulation leads us to the maximum entropy distribution that captures pairwise phase relationships. To solve the inverse problem for this distribution, we derive a closed-form solution for estimating the phase coupling parameters from observed phase statistics. Through simulations, we show that the algorithm performs well in high dimensions (d = 100) and in cases with limited data (as few as 100 samples per dimension). In addition, we derive a regularized solution to the estimation and show that the resulting procedure improves performance when only a limited amount of data is available. Because the distribution serves as the unique maximum entropy solution for pairwise phase statistics, phase coupling estimation can be broadly applied in any situation where phase measurements are made. Under the physical interpretation, the model may be used for inferring coupling relationships within cortical networks.

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Foxe, John J., Adam C. Snyder, Manuel R. Mercier, John S. Butler, Sophie Molholm, and Ian C. Fiebelkorn. "Cross-sensory cuing drives cross-frequency neural coupling, dramatically altering performance of a taxing visual-detection task." Seeing and Perceiving 25 (2012): 62. http://dx.doi.org/10.1163/187847612x646839.

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Functional networks are comprised of neuronal ensembles bound through synchronization across multiple intrinsic oscillatory frequencies. Various coupled interactions between brain oscillators have been described (e.g., phase–amplitude coupling), but with little evidence that these interactions actually influence perceptual sensitivity. Here, electroencephalographic recordings were made during a sustained-attention task to demonstrate that cross-frequency coupling, driven by cross-sensory cuing, has significant consequences for perceptual outcomes (i.e., whether participants detect a near-threshold visual target). Our results reveal that phase-detection relationships at higher frequencies are entirely dependent on the phase of lower frequencies, such that higher frequencies alternate between periods when their phase is strongly predictive of visual-target detection and periods when their phase has no influence whatsoever. These data thus bridge the crucial gap between complex oscillatory phenomena and perceptual outcomes. Accounting for cross-frequency coupling between lower (i.e., delta and theta) and higher frequencies (e.g., beta and gamma), we show that visual-target detection fluctuates dramatically as a function of pre-stimulus phase, with performance swings of as much as 80%.

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Plotnikov, S. A., J. Lehnert, A. L. Fradkov, and E. Schöll. "Adaptive Control of Synchronization in Delay-Coupled Heterogeneous Networks of FitzHugh–Nagumo Nodes." International Journal of Bifurcation and Chaos 26, no. 04 (April 2016): 1650058. http://dx.doi.org/10.1142/s0218127416500589.

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We study synchronization in delay-coupled neural networks of heterogeneous nodes. It is well known that heterogeneities in the nodes hinder synchronization when becoming too large. We show that an adaptive tuning of the overall coupling strength can be used to counteract the effect of the heterogeneity. Our adaptive controller is demonstrated on ring networks of FitzHugh–Nagumo systems which are paradigmatic for excitable dynamics but can also — depending on the system parameters — exhibit self-sustained periodic firing. We show that the adaptively tuned time-delayed coupling enables synchronization even if parameter heterogeneities are so large that excitable nodes coexist with oscillatory ones.

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Zou, Wei, Yuxuan Chen, D. V. Senthilkumar, and Jürgen Kurths. "Oscillation quenching in diffusively coupled dynamical networks with inertial effects." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 4 (April 2022): 041102. http://dx.doi.org/10.1063/5.0087839.

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Self-sustained oscillations are ubiquitous and of fundamental importance for a variety of physical and biological systems including neural networks, cardiac dynamics, and circadian rhythms. In this work, oscillation quenching in diffusively coupled dynamical networks including “inertial” effects is analyzed. By adding inertia to diffusively coupled first-order oscillatory systems, we uncover that even small inertia is capable of eradicating the onset of oscillation quenching. We consolidate the generality of inertia in eradicating oscillation quenching by extensively examining diverse quenching scenarios, where macroscopic oscillations are extremely deteriorated and even completely lost in the corresponding models without inertia. The presence of inertia serves as an additional scheme to eradicate the onset of oscillation quenching, which does not need to tailor the coupling functions. Our findings imply that inertia of a system is an enabler against oscillation quenching in coupled dynamical networks, which, in turn, is helpful for understanding the emergence of rhythmic behaviors in complex coupled systems with amplitude degree of freedom.

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Canolty, Ryan T., Charles F. Cadieu, Kilian Koepsell, Karunesh Ganguly, Robert T. Knight, and Jose M. Carmena. "Detecting event-related changes of multivariate phase coupling in dynamic brain networks." Journal of Neurophysiology 107, no. 7 (April 1, 2012): 2020–31. http://dx.doi.org/10.1152/jn.00610.2011.

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Oscillatory phase coupling within large-scale brain networks is a topic of increasing interest within systems, cognitive, and theoretical neuroscience. Evidence shows that brain rhythms play a role in controlling neuronal excitability and response modulation (Haider B, McCormick D. Neuron 62: 171–189, 2009) and regulate the efficacy of communication between cortical regions (Fries P. Trends Cogn Sci 9: 474–480, 2005) and distinct spatiotemporal scales (Canolty RT, Knight RT. Trends Cogn Sci 14: 506–515, 2010). In this view, anatomically connected brain areas form the scaffolding upon which neuronal oscillations rapidly create and dissolve transient functional networks (Lakatos P, Karmos G, Mehta A, Ulbert I, Schroeder C. Science 320: 110–113, 2008). Importantly, testing these hypotheses requires methods designed to accurately reflect dynamic changes in multivariate phase coupling within brain networks. Unfortunately, phase coupling between neurophysiological signals is commonly investigated using suboptimal techniques. Here we describe how a recently developed probabilistic model, phase coupling estimation (PCE; Cadieu C, Koepsell K Neural Comput 44: 3107–3126, 2010), can be used to investigate changes in multivariate phase coupling, and we detail the advantages of this model over the commonly employed phase-locking value (PLV; Lachaux JP, Rodriguez E, Martinerie J, Varela F. Human Brain Map 8: 194–208, 1999). We show that the N-dimensional PCE is a natural generalization of the inherently bivariate PLV. Using simulations, we show that PCE accurately captures both direct and indirect (network mediated) coupling between network elements in situations where PLV produces erroneous results. We present empirical results on recordings from humans and nonhuman primates and show that the PCE-estimated coupling values are different from those using the bivariate PLV. Critically on these empirical recordings, PCE output tends to be sparser than the PLVs, indicating fewer significant interactions and perhaps a more parsimonious description of the data. Finally, the physical interpretation of PCE parameters is straightforward: the PCE parameters correspond to interaction terms in a network of coupled oscillators. Forward modeling of a network of coupled oscillators with parameters estimated by PCE generates synthetic data with statistical characteristics identical to empirical signals. Given these advantages over the PLV, PCE is a useful tool for investigating multivariate phase coupling in distributed brain networks.

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Song, Yongli, Valeri A. Makarov, and Manuel G. Velarde. "Stability switches, oscillatory multistability, and spatio-temporal patterns of nonlinear oscillations in recurrently delay coupled neural networks." Biological Cybernetics 101, no. 2 (July 21, 2009): 147–67. http://dx.doi.org/10.1007/s00422-009-0326-5.

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Hurtado, Jose M., Leonid L. Rubchinsky, and Karen A. Sigvardt. "Statistical Method for Detection of Phase-Locking Episodes in Neural Oscillations." Journal of Neurophysiology 91, no. 4 (April 2004): 1883–98. http://dx.doi.org/10.1152/jn.00853.2003.

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In many networks of oscillatory neurons, synaptic interactions can promote the entrainment of units into phase-coupled groups. The detection of synchrony in experimental data, especially if the data consist of single-trial runs, can be problematic when, for example, phase entrainment is of short duration, buried in noise, or masked by amplitude fluctuations that are uncorrelated among the oscillating units. In the present study, we tackle the problem of detecting neural interactions from pairs of oscillatory signals in a narrow frequency band. To avoid the interference of amplitude fluctuations in the detection of synchrony, we extract a phase variable from the data and utilize statistical indices to measure phase locking. We use three different phase-locking indices based on coherence, entropy, and mutual information between the phase variables. Phase-locking indices are calculated over time using sliding analysis windows. By varying the duration of the analysis windows, we were able to inspect the data at different levels of temporal resolution and statistical reliability. The statistical significance of high index values was evaluated using four different surrogate data methods. We determined phase-locking indices using alternative methods for generating surrogate data and found that results are sensitive to the particular method selected. Surrogate methods that preserve the temporal structure of the individual phase time series decrease substantially the number of false positives when tested on a pair of independent signals.

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Eckhorn, R., H. J. Reitboeck, M. Arndt, and P. Dicke. "Feature Linking via Synchronization among Distributed Assemblies: Simulations of Results from Cat Visual Cortex." Neural Computation 2, no. 3 (September 1990): 293–307. http://dx.doi.org/10.1162/neco.1990.2.3.293.

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We recently discovered stimulus-specific interactions between cell assemblies in cat primary visual cortex that could constitute a global linking principle for feature associations in sensory and motor systems: stimulus-induced oscillatory activities (35-80 Hz) in remote cell assemblies of the same and of different visual cortex areas mutually synchronize, if common stimulus features drive the assemblies simultaneously. Based on our neurophysiological findings we simulated feature linking via synchronizations in networks of model neurons. The networks consisted of two one-dimensional layers of neurons, coupled in a forward direction via feeding connections and in lateral and backward directions via modulatory linking connections. The models' performance is demonstrated in examples of region linking with spatiotemporally varying inputs, where the rhythmic activities in response to an input, that initially are uncorrelated, become phase locked. We propose that synchronization is a general principle for the coding of associations in and among sensory systems and that at least two distinct types of synchronization do exist: stimulus-forced (event-locked) synchronizations support “crude instantaneous” associations and stimulus-induced (oscillatory) synchronizations support more complex iterative association processes. In order to bring neural linking mechanisms into correspondence with perceptual feature linking, we introduce the concept of the linking field (association field) of a local assembly of visual neurons. The linking field extends the concept of the invariant receptive field (RF) of single neurons to the flexible association of RFs in neural assemblies.

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Campbell, Shannon R., DeLiang L. Wang, and Ciriyam Jayaprakash. "Synchrony and Desynchrony in Integrate-and-Fire Oscillators." Neural Computation 11, no. 7 (October 1, 1999): 1595–619. http://dx.doi.org/10.1162/089976699300016160.

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Due to many experimental reports of synchronous neural activity in the brain, there is much interest in understanding synchronization in networks of neural oscillators and its potential for computing perceptual organization. Contrary to Hopfield and Herz (1995), we find that networks of locally coupled integrate-and-fire oscillators can quickly synchronize. Furthermore, we examine the time needed to synchronize such networks. We observe that these networks synchronize at times proportional to the logarithm of their size, and we give the parameters used to control the rate of synchronization. Inspired by locally excitatory globally inhibitory oscillator network (LEGION) dynamics with relaxation oscillators (Terman & Wang, 1995), we find that global inhibition can play a similar role of desynchronization in a network of integrate-and-fire oscillators. We illustrate that a LEGION architecture with integrate-and-fire oscillators can be similarly used to address image analysis.

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Granada, Adrián E., Trinitat Cambras, Antoni Díez-Noguera, and Hanspeter Herzel. "Circadian desynchronization." Interface Focus 1, no. 1 (November 17, 2010): 153–66. http://dx.doi.org/10.1098/rsfs.2010.0002.

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The suprachiasmatic nucleus (SCN) coordinates via multiple outputs physiological and behavioural circadian rhythms. The SCN is composed of a heterogeneous network of coupled oscillators that entrain to the daily light–dark cycles. Outside the physiological entrainment range, rich locomotor patterns of desynchronized rhythms are observed. Previous studies interpreted these results as the output of different SCN neural subpopulations. We find, however, that even a single periodically driven oscillator can induce such complex desynchronized locomotor patterns. Using signal analysis, we show how the observed patterns can be consistently clustered into two generic oscillatory interaction groups: modulation and superposition. In seven of 17 rats undergoing forced desynchronization, we find a theoretically predicted third spectral component. Combining signal analysis with the theory of coupled oscillators, we provide a framework for the study of circadian desynchronization.

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UETA, TETSUSHI, and HIROSHI KAWAKAMI. "BIFURCATION IN ASYMMETRICALLY COUPLED BVP OSCILLATORS." International Journal of Bifurcation and Chaos 13, no. 05 (May 2003): 1319–27. http://dx.doi.org/10.1142/s0218127403007199.

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BVP oscillator is the simplest mathematical model describing dynamical behavior of neural activity. Large scale neural network can often be described naturally by coupled systems of BVP oscillators. However, even if two BVP oscillators are merely coupled by a linear element, the whole system exhibits complicated behavior. In this letter, we analyze coupled BVP oscillators with asymmetrical coupling structure, besides, each oscillator has different internal resistance. The system shows a rich variety of bifurcation phenomena and strange attractors. We calculate bifurcation diagrams in two-parameter plane around which the chaotic attractors mainly appear and confirm relaxant phenomena in the laboratory experiments. We also briefly report a conspicuous strange attractor.

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Haqiqatkhah, MohamamdHossein Manuel, and Cees van Leeuwen. "Adaptive rewiring in nonuniform coupled oscillators." Network Neuroscience 6, no. 1 (2022): 90–117. http://dx.doi.org/10.1162/netn_a_00211.

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Abstract Structural plasticity of the brain can be represented in a highly simplified form as adaptive rewiring, the relay of connections according to the spontaneous dynamic synchronization in network activity. Adaptive rewiring, over time, leads from initial random networks to brain-like complex networks, that is, networks with modular small-world structures and a rich-club effect. Adaptive rewiring has only been studied, however, in networks of identical oscillators with uniform or random coupling strengths. To implement information-processing functions (e.g., stimulus selection or memory storage), it is necessary to consider symmetry-breaking perturbations of oscillator amplitudes and coupling strengths. We studied whether nonuniformities in amplitude or connection strength could operate in tandem with adaptive rewiring. Throughout network evolution, either amplitude or connection strength of a subset of oscillators was kept different from the rest. In these extreme conditions, subsets might become isolated from the rest of the network or otherwise interfere with the development of network complexity. However, whereas these subsets form distinctive structural and functional communities, they generally maintain connectivity with the rest of the network and allow the development of network complexity. Pathological development was observed only in a small proportion of the models. These results suggest that adaptive rewiring can robustly operate alongside information processing in biological and artificial neural networks.

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Powanwe, Arthur S., and Andre Longtin. "Mechanisms of Flexible Information Sharing through Noisy Oscillations." Biology 10, no. 8 (August 10, 2021): 764. http://dx.doi.org/10.3390/biology10080764.

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Brain areas must be able to interact and share information in a time-varying, dynamic manner on a fast timescale. Such flexibility in information sharing has been linked to the synchronization of rhythm phases between areas. One definition of flexibility is the number of local maxima in the delayed mutual information curve between two connected areas. However, the precise relationship between phase synchronization and information sharing is not clear, nor is the flexibility in the face of the fixed structural connectivity and noise. Here, we consider two coupled oscillatory excitatory-inhibitory networks connected through zero-delay excitatory connections, each of which mimics a rhythmic brain area. We numerically compute phase-locking and delayed mutual information between the phases of excitatory local field potential (LFPs) of the two networks, which measures the shared information and its direction. The flexibility in information sharing is shown to depend on the dynamical origin of oscillations, and its properties in different regimes are found to persist in the presence of asymmetry in the connectivity as well as system heterogeneity. For coupled noise-induced rhythms (quasi-cycles), phase synchronization is robust even in the presence of asymmetry and heterogeneity. However, they do not show flexibility, in contrast to noise-perturbed rhythms (noisy limit cycles), which are shown here to exhibit two local information maxima, i.e., flexibility. For quasi-cycles, phase difference and information measures for the envelope-phase dynamics obtained from previous analytical work using the Stochastic Averaging Method (SAM) are found to be in good qualitative agreement with those obtained from the original dynamics. The relation between phase synchronization and communication patterns is not trivial, particularly in the noisy limit cycle regime. There, complex patterns of information sharing can be observed for a single value of the phase difference. The mechanisms reported here can be extended to I-I networks since their phase synchronizations are similar. Our results set the stage for investigating information sharing between several connected noisy rhythms in neural and other complex biological networks.

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Cressman, A. J., W. Wattanapanitch, I. Chuang, and R. Sarpeshkar. "Formulation and Emulation of Quantum-Inspired Dynamical Systems With Classical Analog Circuits." Neural Computation 34, no. 4 (March 23, 2022): 856–90. http://dx.doi.org/10.1162/neco_a_01481.

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Abstract Quantum dynamical systems are capable of powerful computation but are hard to emulate on digital computers. We show that four novel analog circuit parts can emulate the phase-coherent unitary dynamics of such systems. These four parts are: a Planck capacitance analogous to a neuronal membrane capacitance; a quantum admittance element, together with the Planck capacitance, analogous to a neuronal quadrature oscillator; a quantum transadmittance element analogous to a complex neuronal synapse; and a quantum transadmittance mixer element analogous to a complex neuronal synapse with resonant modulation. These parts may be emulated classically, with paired real-value voltages on paired Planck capacitances corresponding to the real and imaginary portions of a probability amplitude; and appropriate paired real-value currents onto these Planck capacitances corresponding to diagonal (admittance), off-diagonal (transadmittance), or controlled off-diagonal (transadmittance mixer) Hamiltonian energy terms. The superposition of 2n simultaneously phase-coherent and symmetric probability-voltage amplitudes with O(n) of these parts, in a tensor-product architecture enables analog emulation of the quantum Fourier transform (QFT). Implementation of our circuits on an analog integrated circuit in a 0.18 μm process yield experimental results consistent with mathematical theory and computer simulations for emulations of NMR, Josephson junction, and QFT dynamics. Our results suggest that linear oscillatory neuronal networks with pairs of complex subthreshold/nonspiking sine and cosine neurons that are coupled together via complex synapses to other such complex neurons can architect quantum-inspired computation with classical analog circuits. Thus, an analog-circuit mapping between quantum and neural computation, both of which exploit analog computation for powerful operation, can enable future synergies between these fields.

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Velichko. "A Method for Evaluating Chimeric Synchronization of Coupled Oscillators and Its Application for Creating a Neural Network Information Converter." Electronics 8, no. 7 (July 4, 2019): 756. http://dx.doi.org/10.3390/electronics8070756.

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This paper presents a new method for evaluating the synchronization of quasi-periodic oscillations of two oscillators, termed “chimeric synchronization”. The family of metrics is proposed to create a neural network information converter based on a network of pulsed oscillators. In addition to transforming input information from digital to analogue, the converter can perform information processing after training the network by selecting control parameters. In the proposed neural network scheme, the data arrives at the input layer in the form of current levels of the oscillators and is converted into a set of non-repeating states of the chimeric synchronization of the output oscillator. By modelling a thermally coupled VO2-oscillator circuit, the network setup is demonstrated through the selection of coupling strength, power supply levels, and the synchronization efficiency parameter. The distribution of solutions depending on the operating mode of the oscillators, sub-threshold mode, or generation mode are revealed. Technological approaches for the implementation of a neural network information converter are proposed, and examples of its application for image filtering are demonstrated. The proposed method helps to significantly expand the capabilities of neuromorphic and logical devices based on synchronization effects.

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Wilson, Hugh R. "Hyperchaos in Wilson–Cowan oscillator circuits." Journal of Neurophysiology 122, no. 6 (December 1, 2019): 2449–57. http://dx.doi.org/10.1152/jn.00323.2019.

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The Wilson–Cowan equations were originally shown to produce limit cycle oscillations for a range of parameters. Others subsequently showed that two coupled Wilson–Cowan oscillators could produce chaos, especially if the oscillator coupling was from inhibitory interneurons of one oscillator to excitatory neurons of the other. Here this is extended to show that chains, grids, and sparse networks of Wilson–Cowan oscillators generate hyperchaos with linearly increasing complexity as the number of oscillators increases. As there is now evidence that humans can voluntarily generate hyperchaotic visuomotor sequences, these results are particularly relevant to the unpredictability of a range of human behaviors. These also include incipient senescence in aging, effects of concussive brain injuries, autism, and perhaps also intelligence and creativity. NEW & NOTEWORTHY This paper represents an exploration of hyperchaos in coupled Wilson–Cowan equations. Results show that hyperchaos (number of positive Lyapunov exponents) grows linearly with the number of oscillators in the array and leads to high levels of unpredictability in the neural response.

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Belyakin, Sergey. "Neural Networks In A Generalized Model Of The N-Pacemaker Phase Response Curve." Neurodegeneration and Neurorehabilitation 3, no. 1 (March 10, 2020): 01–12. http://dx.doi.org/10.31579/2692-9422/005.

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In this publication, we generalize the proposed model of two interacting oscillators in the case of a strong difference in their periods (when the pacemaker pulses do not alternate) and propose a General model describing a network of oscillators coupled globally. Our goal is to make the model as simple as possible and enter the minimum number of parameters. Therefore, we will fully characterize the pacemaker of their internal lengths of the cycle and re-present them as pulse oscillators. Interaction of pacemakers is described by PRC.

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KAZANTSEV, V. B., V. I. NEKORKIN, S. MORFU, J. M. BILBAULT, and P. MARQUIÉ. "PROPAGATING INTERFACES IN A TWO-LAYER BISTABLE NEURAL NETWORK." International Journal of Bifurcation and Chaos 16, no. 03 (March 2006): 589–600. http://dx.doi.org/10.1142/s0218127406015003.

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The dynamics of propagating interfaces in a bistable neural network is investigated. We consider the network composed of two coupled 1D lattices and assume that they interact in a local spatial point (pin contact). The network unit is modeled by the FitzHugh–Nagumo-like system in a bistable oscillator mode. The interfaces describe the transition of the network units from the rest (unexcited) state to the excited state where each unit exhibits periodic sequences of excitation pulses or action potentials. We show how the localized inter-layer interaction provides an "excitatory" or "inhibitory" action to the oscillatory activity. In particular, we describe the interface propagation failure and the initiation of spreading activity due to the pin contact. We provide analytical results, computer simulations and physical experiments with two-layer electronic arrays of bistable cells.

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Amick, C. J. "A problem in neural networks." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 118, no. 3-4 (1991): 225–36. http://dx.doi.org/10.1017/s0308210500029061.

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SynopsisIn this paper we consider a simple model for coupled nonlinear oscillators in a continuous medium. There is shown to exist a maximal branch of phaselocked solutions connecting the trivial one to a limiting singular solution.

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Baldi, Pierre, and Ronny Meir. "Computing with Arrays of Coupled Oscillators: An Application to Preattentive Texture Discrimination." Neural Computation 2, no. 4 (December 1990): 458–71. http://dx.doi.org/10.1162/neco.1990.2.4.458.

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Recent experimental findings (Gray et al. 1989; Eckhorn et al. 1988) seem to indicate that rapid oscillations and phase-lockings of different populations of cortical neurons play an important role in neural computations. In particular, global stimulus properties could be reflected in the correlated firing of spatially distant cells. Here we describe how simple coupled oscillator networks can be used to model the data and to investigate whether useful tasks can be performed by oscillator architectures. A specific demonstration is given for the problem of preattentive texture discrimination. Texture images are convolved with different sets of Gabor filters feeding into several corresponding arrays of coupled oscillators. After a brief transient, the dynamic evolution in the arrays leads to a separation of the textures by a phase labeling mechanism. The importance of noise and of long range connections is briefly discussed.

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Kumpeerakij, Chanin. "Memorization and prediction capability of the interacting phase oscillators." Journal of Physics: Conference Series 2431, no. 1 (January 1, 2023): 012085. http://dx.doi.org/10.1088/1742-6596/2431/1/012085.

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Abstract Nonlinear dynamical systems, such as well-tuned recurrent neural networks, have proved a powerful tool for modeling temporal data. However, tuning such models to achieve optimal performance remains an outstanding challenge, not least because of the complex behaviors that emerge from interacting microscopic constituents. Here, we consider a minimal model of two interacting phase oscillators coupled to a thermal bath and driven by a common signal. We quantify the memory and predictive capability of the system with the mutual information between the phases of oscillators and the signals at different times. We show that the interaction between oscillators can increase the information between the system and the movement. We attribute this behavior to an increase in the effective signal-to-noise ratio, resulting from a stronger correlation between the oscillators. We also demonstrate that heterogeneity in the natural frequencies of the oscillators can further increase the mutual information though more efficient uses of oscillator states.Our work offers the first step toward a systematic approach to optimizing interacting nonlinear dynamical systems for memorizing and predicting temporal patterns.

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Călugăru, Dumitru, Jan Frederik Totz, Erik A. Martens, and Harald Engel. "First-order synchronization transition in a large population of strongly coupled relaxation oscillators." Science Advances 6, no. 39 (September 2020): eabb2637. http://dx.doi.org/10.1126/sciadv.abb2637.

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Onset and loss of synchronization in coupled oscillators are of fundamental importance in understanding emergent behavior in natural and man-made systems, which range from neural networks to power grids. We report on experiments with hundreds of strongly coupled photochemical relaxation oscillators that exhibit a discontinuous synchronization transition with hysteresis, as opposed to the paradigmatic continuous transition expected from the widely used weak coupling theory. The resulting first-order transition is robust with respect to changes in network connectivity and natural frequency distribution. This allows us to identify the relaxation character of the oscillators as the essential parameter that determines the nature of the synchronization transition. We further support this hypothesis by revealing the mechanism of the transition, which cannot be accounted for by standard phase reduction techniques.

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Sharma, Sanjeev Kumar, Arnab Mondal, Argha Mondal, Ranjit Kumar Upadhyay, and Jun Ma. "Synchronization and Pattern Formation in a Memristive Diffusive Neuron Model." International Journal of Bifurcation and Chaos 31, no. 11 (September 2, 2021): 2130030. http://dx.doi.org/10.1142/s0218127421300305.

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In this article, we construct an excitable memristive diffusive neuron model by considering a biophysical slow–fast bursting oscillator and study the effects of electromagnetic induction on the dynamics of the single model as well as the coupled systems. We explore various firing regimes such as tonic spiking, bursting, and mixed-mode oscillations depending on the bifurcation structure with different injected current stimuli, then perform a comparative analysis on the synchronization of the coupled oscillators by setting the model into two different network architectures. First, a diffusively coupled network is considered, and later a global network is constructed. The results suggest that the diffusively connected neurons show complete synchronization at higher couplings for bursting and tonic spiking regimes. Furthermore, we show that the extended spatial system can generate spiral-like patterns in the vicinity of a Hopf bifurcation point and observe the impact of Gaussian white noise to study its effects on pattern formation. These types of patterns are robust in the excitable model. Our results might contribute significantly to the dynamical studies of irregular neural computation.

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Shcherbak, Volodymyr, and Iryna Dmytryshyn. "Estimation of oscillation velocities of oscillator network." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 32 (December 28, 2018): 182–89. http://dx.doi.org/10.37069/1683-4720-2018-32-17.

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The study of the collective behavior of multiscale dynamic processes is currently one of the most urgent problems of nonlinear dynamics. Such systems arise on modelling of many cyclical biological or physical processes. It is of fundamental importance for understanding the basic laws of synchronous dynamics of distributed active subsystems with oscillations, such as neural ensembles, biomechanical models of cardiac or locomotor activity, models of turbulent media, etc. Since the nonlinear oscillations that are observed in such systems have a stable limit cycle , which does not depend on the initial conditions, then a system of interconnected nonlinear oscillators is usually used as a model of multiscale processes. The equations of Lienar type are often used as the main dynamic model of each of these oscillators. In a number of practical control problems of such interconnected oscillators it is necessary to determine the oscillation velocities by known data. This problem is considered as observation problem for nonlinear dynamical system. A new method – a synthesis of invariant relations is used to design a nonlinear observer. The method allows us to represent unknowns as a function of known quantities. The scheme of the construction of invariant relations consists in the expansion of the original dynamical system by equations of some controlled subsystem (integrator). Control in the additional system is used for the synthesis of some relations that are invariant for the extended system and have the attraction property for all of its trajectories. Such relations are considered in observation problems as additional equations for unknown state vector of initial oscillators ensemble. To design the observer, first we introduce a observer for unique oscillator of Lienar type and prove its exponential convergence. This observer is then extended on several coupled Lienar type oscillators. The performance of the proposed method is investigated by numerical simulations.

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Chen, Ke, and DeLiang Wang. "A dynamically coupled neural oscillator network for image segmentation." Neural Networks 15, no. 3 (April 2002): 423–39. http://dx.doi.org/10.1016/s0893-6080(02)00028-x.

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Ly, Cheng, and G. Bard Ermentrout. "Analysis of Recurrent Networks of Pulse-Coupled Noisy Neural Oscillators." SIAM Journal on Applied Dynamical Systems 9, no. 1 (January 2010): 113–37. http://dx.doi.org/10.1137/090756065.

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Zhang, Zhengyuan, and Liming Dai. "Effects of Synaptic Pruning on Phase Synchronization in Chimera States of Neural Network." Applied Sciences 12, no. 4 (February 12, 2022): 1942. http://dx.doi.org/10.3390/app12041942.

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This research explores the effect of synaptic pruning on a ring-shaped neural network of non-locally coupled FitzHugh–Nagumo (FHN) oscillators. The neurons in the pruned region synchronize with each other, and they repel the coherent domain of the chimera states. Furthermore, the width of the pruned region decides the precision and efficiency of the control effect on the position of coherent domains. This phenomenon gives a systematic comprehension of the relation between pruning and synchronization in neural networks from a new aspect that has never been addressed. An explanation of this mechanism is also given.

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Izhikevich, E. M. "Weakly pulse-coupled oscillators, FM interactions, synchronization, and oscillatory associative memory." IEEE Transactions on Neural Networks 10, no. 3 (May 1999): 508–26. http://dx.doi.org/10.1109/72.761708.

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NISHIKAWA, IKUKO, TAKESHI IRITANI, KAZUTOSHI SAKAKIBARA, and YASUAKI KUROE. "PHASE DYNAMICS OF COMPLEX-VALUED NEURAL NETWORKS AND ITS APPLICATION TO TRAFFIC SIGNAL CONTROL." International Journal of Neural Systems 15, no. 01n02 (February 2005): 111–20. http://dx.doi.org/10.1142/s0129065705000062.

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Complex-valued Hopfield networks which possess the energy function are analyzed. The dynamics of the network with certain forms of an activation function is decomposable into the dynamics of the amplitude and phase of each neuron. Then the phase dynamics is described as a coupled system of phase oscillators with a pair-wise sinusoidal interaction. Therefore its phase synchronization mechanism is useful for the area-wide offset control of the traffic signals. The computer simulations show the effectiveness under the various traffic conditions.

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Abrevaya, Germán, Guillaume Dumas, Aleksandr Y. Aravkin, Peng Zheng, Jean-Christophe Gagnon-Audet, James Kozloski, Pablo Polosecki, et al. "Learning Brain Dynamics With Coupled Low-Dimensional Nonlinear Oscillators and Deep Recurrent Networks." Neural Computation 33, no. 8 (July 26, 2021): 2087–127. http://dx.doi.org/10.1162/neco_a_01401.

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Many natural systems, especially biological ones, exhibit complex multivariate nonlinear dynamical behaviors that can be hard to capture by linear autoregressive models. On the other hand, generic nonlinear models such as deep recurrent neural networks often require large amounts of training data, not always available in domains such as brain imaging; also, they often lack interpretability. Domain knowledge about the types of dynamics typically observed in such systems, such as a certain type of dynamical systems models, could complement purely data-driven techniques by providing a good prior. In this work, we consider a class of ordinary differential equation (ODE) models known as van der Pol (VDP) oscil lators and evaluate their ability to capture a low-dimensional representation of neural activity measured by different brain imaging modalities, such as calcium imaging (CaI) and fMRI, in different living organisms: larval zebrafish, rat, and human. We develop a novel and efficient approach to the nontrivial problem of parameters estimation for a network of coupled dynamical systems from multivariate data and demonstrate that the resulting VDP models are both accurate and interpretable, as VDP's coupling matrix reveals anatomically meaningful excitatory and inhibitory interactions across different brain subsystems. VDP outperforms linear autoregressive models (VAR) in terms of both the data fit accuracy and the quality of insight provided by the coupling matrices and often tends to generalize better to unseen data when predicting future brain activity, being comparable to and sometimes better than the recurrent neural networks (LSTMs). Finally, we demonstrate that our (generative) VDP model can also serve as a data-augmentation tool leading to marked improvements in predictive accuracy of recurrent neural networks. Thus, our work contributes to both basic and applied dimensions of neuroimaging: gaining scientific insights and improving brain-based predictive models, an area of potentially high practical importance in clinical diagnosis and neurotechnology.

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DeLiang Wang. "Emergent synchrony in locally coupled neural oscillators." IEEE Transactions on Neural Networks 6, no. 4 (July 1995): 941–48. http://dx.doi.org/10.1109/72.392256.

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Zhang, Fan, Bo Du, Liangpei Zhang, and Miaozhong Xu. "Weakly Supervised Learning Based on Coupled Convolutional Neural Networks for Aircraft Detection." IEEE Transactions on Geoscience and Remote Sensing 54, no. 9 (September 2016): 5553–63. http://dx.doi.org/10.1109/tgrs.2016.2569141.

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Arai, Hiroko, and Hiroshi Imamura. "Spin-wave coupled spin torque oscillators for artificial neural network." Journal of Applied Physics 124, no. 15 (October 21, 2018): 152131. http://dx.doi.org/10.1063/1.5040020.

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Boriskov, P. P., and A. A. Velichko. "Inductively coupled burst oscillators in neural network information processing systems." Journal of Physics: Conference Series 1399 (December 2019): 033051. http://dx.doi.org/10.1088/1742-6596/1399/3/033051.

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YuQiao, Gu, Chen TianLun, and Huang WuQun. "A Neural Network Model with Self-organizing Pulse-Coupled Oscillator." Communications in Theoretical Physics 34, no. 1 (July 30, 2000): 63–68. http://dx.doi.org/10.1088/0253-6102/34/1/63.

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Qiao, Yuanhua, Yong Meng, Lijuan Duan, Faming Fang, and Jun Miao. "Qualitative analysis and application of locally coupled neural oscillator network." Neural Computing and Applications 21, no. 7 (January 21, 2012): 1551–62. http://dx.doi.org/10.1007/s00521-012-0829-1.

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Omel’chenko, O. E. "Periodic orbits in the Ott–Antonsen manifold." Nonlinearity 36, no. 2 (December 16, 2022): 845–61. http://dx.doi.org/10.1088/1361-6544/aca94c.

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Abstract In their seminal paper (2008 Chaos 18 037113), Ott and Antonsen showed that large groups of phase oscillators driven by a certain type of common force display low dimensional long-term dynamics, which is described by a small number of ordinary differential equations. This fact was later used as a simplifying reduction technique in many studies of synchronisation phenomena occurring in networks of coupled oscillators and in neural networks. Most of these studies focused mainly on partially synchronised states corresponding to the equilibrium-type dynamics in the so called Ott–Antonsen manifold. Going beyond this paradigm, here we propose a universal approach for the efficient analysis of partially synchronised states with non-equilibrium periodic collective dynamics. Our method is based on the observation that the Poincaré map of the complex Riccati equation, which describes the dynamics in the Ott–Antonsen manifold, coincides with the well-known Möbius transformation. To illustrate the possibilities of our method, we use it to calculate a complete bifurcation diagram of travelling chimera states in a ring network of phase oscillators with asymmetric nonlocal coupling.

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Journal articles on the topic 'Weakly-coupled Oscillatory Neural Networks'

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