Relevant bibliographies by topics / Weakly-coupled Oscillatory Neural Networks

Academic literature on the topic 'Weakly-coupled Oscillatory Neural Networks'

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Published: 14 March 2023

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Journal articles on the topic "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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Dissertations / Theses on the topic "Weakly-coupled Oscillatory Neural Networks"

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Bradley, Patrick Justin. "Heterogeneously coupled neural oscillators." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/33938.

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The work we present in this thesis is a series of studies of how heterogeneities in coupling affect the synchronization of coupled neural oscillators. We begin by examining how heterogeneity in coupling strength affects the equilibrium phase difference of a pair of coupled, spiking neurons when compared to the case of identical coupling. This study is performed using pairs of Hodgkin-Huxley and Wang-Buzsaki neurons. We find that heterogeneity in coupling strength breaks the symmetry of the bifurcation diagrams of equilibrium phase difference versus the synaptic rate constant for weakly coupled pairs of neurons. We observe important qualitative changes such as the loss of the ubiquitous in-phase and anti-phase solutions found when the coupling is identical and regions of parameter space where no phase locked solution exists. Another type of heterogeneity can be found by having different types of coupling between oscillators. Synaptic coupling between neurons can either be exciting or inhibiting. We examine the synchronization dynamics when a pair of neurons is coupled with one excitatory and one inhibitory synapse. We also use coupled pairs of Hodgkin-Huxley neurons and Wang-Buzsaki neurons for this work. We then explore the existance of 1:n coupled states for a coupled pair of theta neurons. We do this in order to reproduce an observed effect called quantal slowing. Quantal slowing is the phenomena where jumping between different $1:n$ coupled states is observed instead of gradual changes in period as a parameter in the system is varied. All of these topics fall under the general heading of coupled, non-linear oscillators and specifically weakly coupled, neural oscillators. The audience for this thesis is most likely going to be a mixed crowd as the research reported herein is interdisciplinary. Choosing the content for the introduction proved far more challenging than expected. It might be impossible to write a maximally useful introductory portion of a thesis when it could be read by a physicist, mathematician, engineer or biologist. Undoubtedly readers will find some portion of this introduction elementary. At the risk of boring some or all of my readers we decided it was best to proceed so that enough of the mathematical (biological) background is explained in the introduction so that a biologist (mathematician) is able to appreciate the motivations for the research and the results presented. We begin with a introduction in nonlinear dynamics explaining the mathematical tools we use to characterize the excitability of individual neurons, as well as oscillations and synchrony in neural networks. The next part of the introductory material is an overview of the biology of neurons. We then describe the neuron models used in this work and finally describe the techniques we employ to study coupled neurons.
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Hölzel, Robert [Verfasser], Katharina [Akademischer Betreuer] Krischer, and Arkady [Akademischer Betreuer] Pikovsky. "A Neural Network of Weakly Coupled Nonlinear Oscillators with a Global, Time-Dependent Coupling - Theory and Experiment / Robert Hölzel. Gutachter: Arkady Pikovsky ; Katharina Krischer. Betreuer: Katharina Krischer." München : Universitätsbibliothek der TU München, 2013. http://d-nb.info/1034641972/34.

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Sandmann, Humberto Rodrigo. "Padrões de pulsos e computação em redes neurais com dinâmica." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/3/3142/tde-05092012-165022/.

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O processamento de sinais feito pelos sistemas neurais biológicos é altamente eficiente e complexo, por isso desperta grande atenção de pesquisa. Basicamente, todo o processamento de sinais funciona com base em redes de neurônios que emitem e recebem pulsos. Portanto, de forma geral, os estímulos recebidos do sistema sensorial por uma rede neural biológica de algum modo são convertidos em trens de pulsos. Aqui, nesta tese, é apresentada uma nova arquitetura composta por duas camadas: a primeira recebe correntes de estímulos de entrada e os mapeia em trens de pulsos; a segunda recebe esses trens de pulsos e os clássica em conjuntos de estímulos. Na primeira camada, a conversão de correntes de estímulos em trens de pulso é feita através de uma rede de neurônios osciladores acoplados por pulso. Esses neurônios possuem uma frequência natural de disparo e quando são agrupados em redes podem se coordenar para apresentar uma dinâmica global a longo prazo. Por sua vez, a dinâmica global também é sensível às correntes de entrada. Na segunda camada, a classificação dos trens de pulsos em conjuntos de estímulos é implementada por um neurônio do tipo integra-e-dispara. O comportamento típico para esse neurônio é de disparar ao menos uma vez para todas as integrações de trens de pulsos de uma determinada classe; caso contrário, ele deve car em silêncio. O processo de aprendizado da segunda camada depende do conhecimento do intervalo de tempo de repetição de um trem de pulsos. Portanto, nesta tese, são apresentadas métricas para definir tal intervalo de tempo, dando, assim, autonomia para a arquitetura. É possível concluir com base nos ensaios realizados que a arquitetura desenvolvida possui uma grande capacidade para mapeamento de correntes de entradas em trens de pulsos sem a necessidade de alterações na estrutura da arquitetura; também que a adição da dimensão tempo pela primeira camada ajuda na classificação realizada pela segunda. Assim, um novo modelo para realizar processos de codificação e decodificação é apresentado, desenvolvido através de séries de ensaios computacionais e caracterizado por medidas de sua dinâmica.
The signal processing done by the neural systems is highly efficient and complex, so that it attracts a large attention for research. Basically, all the signal processing functions are based on networks of neurons that send and receive spikes. Therefore, in general, the stimuli received from the sensory system by a biological neural network somehow are converted into spike trains. Here, in this thesis, we present a new architecture composed of two layers: the first layer receives streams of input stimuli and maps them on spike trains; the second layer receives these spike trains and classifies them in a sets of stimuli. In the first layer, the conversion of currents of stimuli on spike trains is made by a pulse-coupled neural network. Neurons in this context are like oscillators and have a natural frequency to shoot; when they are grouped into networks, they can be coordinated to present a global long-term dynamics. In turn, this global dynamics is also sensible to the input currents. In the second layer, the classification of spike trains in sets of stimuli is implemented by an integrate-and-re neuron. The typical behavior for this neuron is to shoot at least once every time that it receives a known spike train; otherwise, it should be in silence. The learning process of the second layer depends on the knowledge of the time interval of repetition of a spike train. Therefore, in this thesis, metrics are presented to define this time interval, thus giving autonomy to the architecture. It can be concluded on the basis of the tests developed that the architecture has a large capacity for mapping input currents on spike trains without requiring changes in its structure; moreover, the addition of the time dimension done by the first layer helps in the classification performed by the second layer. Thus, a new model to perform the encoding and decoding processes is presented, developed through a series of computational experiments and characterized by measurements of its dynamics.
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Devalle, Federico. "Collective phenomena in networks of spiking neurons with synaptic delays." Doctoral thesis, Universitat Pompeu Fabra, 2019. http://hdl.handle.net/10803/666912.

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A prominent feature of the dynamics of large neuronal networks are the synchrony-driven collective oscillations generated by the interplay between synaptic coupling and synaptic delays. This thesis investigates the emergence of delay-induced oscillations in networks of heterogeneous spiking neurons. Building on recent theoretical advances in exact mean field reductions for neuronal networks, this work explores the dynamics and bifurcations of an exact firing rate model with various forms of synaptic delays. In parallel, the results obtained using the novel firing rate model are compared with extensive numerical simulations of large networks of spiking neurons, which confirm the existence of numerous synchrony-based oscillatory states. Some of these states are novel and display complex forms of partial synchronization and collective chaos. Given the well-known limitation of traditional firing rate models to describe synchrony-based oscillations, previous studies greatly overlooked many of the oscillatory states found here. Therefore, this thesis provides a unique exploration of the oscillatory scenarios found in neuronal networks due to the presence of delays, and may substantially extend the mathematical tools available for modeling the plethora of oscillations detected in electrical recordings of brain activity.
Una característica fonamental de la dinàmica d'una xarxa neuronal és l'emergència d'oscil·lacions degudes a sincronització. L'origen d'aquestes oscil·lacions és molt sovint degut les interaccions sinàptiques i als seus retards temporals inherents. Aquesta tesi analitza la emergència d'oscil·lacions produïdes per retards sinàptics en xarxes neuronals heterogènies. A partir de troballes recents en teories de camp mig per xarxes neuronals, aquest treball explora la dinàmica i les bifurcacions d'un model de {\it rate} amb diferents tipus de retards sinàptics. En paral·lel els resultats obtinguts mitjançant el nou model de rate són comparats amb simulacions numèriques de grans xarxes neuronals. Aquestes simulacions confirmen l'existència de nombrosos estats oscil·latoris produïts per sincronització. Alguns d'aquests estats són nous I mostren formes complexes de sincronització parcial i de caos col·lectiu. Gran part d'aquestes oscil·lacions han estat àmpliament ignorades a la literatura, degut a la limitació dels models tradicionals de rate per descriure estats amb un alt nivell de sincronització. Així doncs aquesta tesi ofereix una exploració única dels possibles escenaris oscil·latoris en xarxes neuronals amb retards sinàptics, i amplia significativament les eines matemàtiques disponibles per a la modelització de la gran diversitat d'oscil·lacions neuronals presents en les mesures elèctriques de l'activitat cerebral.
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Timme, Marc. "Collective Dynamics in Networks of Pulse-Coupled Oscillators." Doctoral thesis, 2002. http://hdl.handle.net/11858/00-1735-0000-0006-B575-5.

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Kirst, Christoph. "Synchronization, Neuronal Excitability, and Information Flow in Networks of Neuronal Oscillators." Doctoral thesis, 2011. http://hdl.handle.net/11858/00-1735-0000-000D-F08D-2.

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Zalay, Osbert C. "Cognitive Rhythm Generators for Modelling and Modulation of Neuronal Electrical Activity." Thesis, 2012. http://hdl.handle.net/1807/33891.

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An innovative mathematical architecture for modelling neuronal electrical activity is presented, called the cognitive rhythm generator (CRG), wherein the proposed architecture is a hybrid model comprised of three interconnected stages, namely: (1) a bank of neuronal modes; (2) a ring device (limit-cycle oscillator); and (3) a static output nonlinearity (mapper). Coupled CRG networks are employed to emulate and elucidate the dynamics of biological neural networks, including the recurrent networks in the hippocampus. Several species of ring devices are described and investigated, including the clock, labile clock, hourglass and multistable ring systems, and their applications to neuronal modelling explored. Complexity measures such as the maximum Lyapunov exponent, correlation dimension and detrended fluctuation analysis are applied to compare model and biological records and validate the CRG methodology. The basis of neural coding is also examined in mathematical detail, with particular regard to its description by Volterra-Wiener kernel formalism, from which the neuronal modes are derived. Applications to theta-gamma coding are discussed. Further on in the thesis, a CRG epileptiform network model of spontaneous seizure-like events (SLEs) is developed and used as a platform to test neuromodulation approaches for seizure abatement. (Neuromodulation mentioned here refers to methods involving electrical stimulation of neural tissue for therapeutic benefit). Spontaneous SLE transitions in the epileptiform network are shown to be related to the mechanism of intermittency, as determined by examining the state space dynamics of the model. The onset of SLEs is associated with increased network excitability and decreased stability, consistent with experimental results from the low-magnesium/high-potassium in vitro model of epilepsy. Lastly, a novel strategy for therapeutic neuromodulation is presented wherein a coupled CRG network (called the “therapeutic network”) is interfaced with the epileptiform network model, forming a closed loop for responsive, biomimetic neuromodulation of the epileptiform network. Relevance to clinical applications and future work is discussed.
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Schittler, Neves Fabio. "Universal Computation and Memory by Neural Switching." Doctoral thesis, 2010. http://hdl.handle.net/11858/00-1735-0000-0006-B5D1-6.

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Books on the topic "Weakly-coupled Oscillatory Neural Networks"

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1931-, Taylor John Gerald, and Mannion C. L. T, eds. Coupled oscillating neurons. London: Springer-Verlag, 1992.

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Book chapters on the topic "Weakly-coupled Oscillatory Neural Networks"

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Ichiki, Akihisa, and Yasuomi D. Sato. "A Phase Reduction Method for Weakly Coupled Stochastic Oscillator Systems." In Advances in Neural Networks – ISNN 2011, 251–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21105-8_30.

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Isokawa, Teijiro, Haruhiko Nishimura, Naotake Kamiura, and Nobuyuki Matsui. "Perceptual Binding by Coupled Oscillatory Neural Network." In Artificial Neural Networks: Biological Inspirations – ICANN 2005, 139–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11550822_23.

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Baird, Bill. "Information Processing by Dynamical Interaction of Oscillatory Modes in Coupled Cortical Networks." In Neural Network Dynamics, 191–207. London: Springer London, 1992. http://dx.doi.org/10.1007/978-1-4471-2001-8_14.

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Gencic, T., and G. Dangelmayr. "Oscillatory States in Coupled Neural Oscillators." In International Neural Network Conference, 598. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0643-3_15.

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Hoppensteadt, Frank C., and Eugene M. Izhikevich. "Weakly Connected Oscillators." In Weakly Connected Neural Networks, 247–93. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-1828-9_9.

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Hyde, Julie. "Coupled Neuronal Oscillatory Systems." In Neural Network Dynamics, 170–79. London: Springer London, 1992. http://dx.doi.org/10.1007/978-1-4471-2001-8_12.

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Borisyuk, Galina N., Roman M. Borisyuk, and Alexander I. Khibnik. "Analysis of Oscillatory Regimes of a Coupled Neural Oscillator System with Application to Visual Cortex Modeling." In Neural Network Dynamics, 208–25. London: Springer London, 1992. http://dx.doi.org/10.1007/978-1-4471-2001-8_15.

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Baldi, Pierre, Joachim Buhmann, and Ronny Meir. "Computing with Arrays of Coupled Oscillators." In International Neural Network Conference, 908–11. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0643-3_126.

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Irifune, Mayumi, and Robert H. Fujii. "Phase Control of Coupled Neuron Oscillators." In Artificial Neural Networks and Machine Learning – ICANN 2013, 296–303. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-40728-4_37.

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Meng, Yong, Yuanhua Qiao, Jun Miao, Lijuan Duan, and Faming Fang. "Qualitative Analysis in Locally Coupled Neural Oscillator Network." In Advances in Cognitive Neurodynamics (II), 233–37. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-90-481-9695-1_36.

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Conference papers on the topic "Weakly-coupled Oscillatory Neural Networks"

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Farhat, Nabil H., and Mostafa Eldefrawy. "The bifurcating neuron." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.mk3.

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Present neural network models ignore temporal considerations, and hence synchronicity in neural networks, by representing neuron response with a transfer function relating frequency of action potentials (firing frequency) to activation potential. Models of living neuron based on the Hudgkin-Huxley model of the excitable membrane of the squid’s axon and its Fitzhugh-Nagumo approximation, exhibit much more complex and rich behavior than that described by firing frequency-activation potential models. We describe the theory, operation, and properties of an integrate-and-fire neuron which we call the bifurcating neuron and show it has rich complex behavior capable of exhibiting synchronous firing or phase-locked operation, periodic firing, chaotic firing, bursting, and bifurcation between these modes of operation. An optoelectronic realization of the bifurcating neuron in the form of a nonlinear relaxation oscillator is described and experimental verification of its behavior is presented. The circuit shows that bifurcating neuron networks could be easier to construct than sigmoidal neuron networks. A population of bifurcating neurons, coupled through a connection matrix, represent a bifurcating neural network that is expected to exhibit properties not normally observed in networks of sigmoidal neurons. These include feature binding, cognition, quenching, and chaos, all of which play a role in higher level brain function. We expect the bifurcating neuron will lead to a new generation of neural networks more neuromorphic and hence more powerful than networks being dealt with today and that optics will play a role in the implementation of bifurcating neuron networks.
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Herzog, Andreas, Karsten Kube, Bernd Michaelis, Ana D. de Lima, and Thomas Voigt. "Structural adaptation in young neocortical networks modeled by spatially coupled oscillators." In 2007 International Joint Conference on Neural Networks. IEEE, 2007. http://dx.doi.org/10.1109/ijcnn.2007.4371445.

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Vodenicarevic, Damir, Nicolas Locatelli, Julie Grollier, and Damien Querlioz. "Synchronization detection in networks of coupled oscillators for pattern recognition." In 2016 International Joint Conference on Neural Networks (IJCNN). IEEE, 2016. http://dx.doi.org/10.1109/ijcnn.2016.7727447.

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Michaelis, B., A. Herzog, K. Kube, A. D. de Lima, and T. Voigt. "Simulation of young neocortical networks by spatially coupled oscillators." In The 2006 IEEE International Joint Conference on Neural Network Proceedings. IEEE, 2006. http://dx.doi.org/10.1109/ijcnn.2006.246668.

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Toland, Andrew H., Lars A. Holstrom, and George G. Lendaris. "Effectiveness of a Coupled Oscillator Network for Surface Discernment by a Quadruped Robot based on Kinesthetic Experience." In 2007 International Joint Conference on Neural Networks. IEEE, 2007. http://dx.doi.org/10.1109/ijcnn.2007.4371294.

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Uwate, Y., and Y. Nishio. "Complex Phase Synchronization in an Array of Oscillators Coupled by Time-Varying Resistor." In The 2006 IEEE International Joint Conference on Neural Network Proceedings. IEEE, 2006. http://dx.doi.org/10.1109/ijcnn.2006.246994.

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Torikai, H., and T. Saito. "Pulse-coupled networks of non-autonomous integrate-and-fire oscillators and classification functions." In Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium. IEEE, 2000. http://dx.doi.org/10.1109/ijcnn.2000.861318.

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Zhang, Ting, Mohammad R. Haider, Iwan D. Alexander, and Yehia Massoud. "A Coupled Schmitt Trigger Oscillator Neural Network for Pattern Recognition Applications." In 2018 IEEE 61st International Midwest Symposium on Circuits and Systems (MWSCAS). IEEE, 2018. http://dx.doi.org/10.1109/mwscas.2018.8624010.

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Takeda, Kentaro, and Hiroyuki Torikai. "A novel hardware-efficient CPG model for a hexapod robot based on nonlinear dynamics of coupled asynchronous cellular automaton oscillators." In 2019 International Joint Conference on Neural Networks (IJCNN). IEEE, 2019. http://dx.doi.org/10.1109/ijcnn.2019.8852174.

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Yeniceri, Ramazan, and Mustak E. Yalcin. "An implementation of 2D locally coupled relaxation oscillators on an FPGA for real-time autowave generation." In 2008 11th International Workshop on Cellular Neural Networks and Their Applications - CNNA 2008. IEEE, 2008. http://dx.doi.org/10.1109/cnna.2008.4588645.

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