Journal articles: 'Spatio-temporal dynamical systems'

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Uhl, C., F. Kruggel, and D. Y. von Cramon. "Dynamical Systems Based Spatio-Temporal EEG/MEG Modeling." NeuroImage 7, no. 4 (May 1998): S675. http://dx.doi.org/10.1016/s1053-8119(18)31508-8.

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Rod, D. L., and B. D. Sleeman. "Complexity in spatio-temporal dynamics." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 5 (1995): 959–74. http://dx.doi.org/10.1017/s0308210500022587.

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Complex and chaotic structures in certain dynamical systems in biology arise as a consequence of noncomplete integrability of two-degree-of-freedom Hamiltonian systems. A study of this problem is made using Ziglin theory and implemented with the aid of the Kovacic algorithm.

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GUO, YUZHU, L. Z. GUO, S. A. BILLINGS, DANIEL COCA, and Z. Q. LANG. "CHARACTERIZING NONLINEAR SPATIO-TEMPORAL SYSTEMS IN THE FREQUENCY DOMAIN." International Journal of Bifurcation and Chaos 22, no. 02 (February 2012): 1230009. http://dx.doi.org/10.1142/s0218127412300091.

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In this paper a new concept, spatio-temporal generalized frequency response functions (STGFRF), is introduced for the first time to characterize nonlinear spatio-temporal dynamical systems in the frequency domain. A probing method is developed to calculate the STGFRFs recursively for both continuous and discrete spatio-temporal systems. The algorithm is computationally compact and exposes the explicit relationship between the continuous and discrete models and the elements of the generalized frequency response functions.

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Guo, L. Z., and S. A. Billings. "Identification and analysis of spatio-temporal dynamical systems using wavelets." International Journal of Systems Science 39, no. 3 (March 2008): 315–34. http://dx.doi.org/10.1080/00207720701806089.

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DAYA SAGAR, B. S., and C. BABU RAO. "EDITORIAL." International Journal of Pattern Recognition and Artificial Intelligence 17, no. 02 (March 2003): 163–65. http://dx.doi.org/10.1142/s0218001403002289.

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Natural systems undergo several morphological changes with time. To study spatio-temporal dynamics of such natural systems, and to further understand the morphological dynamical behaviors, various images that show several macro- and micro-level phenomena, acquired by various types of sensors need to be analyzed in spatio-temporal scales. Such analyses, to facilitate the researcher to model the spatio-temporal organization of a desired phenomenon, evidently require the robust procedures to extract specific error-free features from multiscale-temporal images represented in discrete space. Geometry and topology based features, such as edges of unique type and general type, are the indicators to record the changes that occur temporally. Extraction of such information is essential prerequisite to develop cogent models to understand the spatio-temporal organization.

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McDermott, Patrick, and Christopher Wikle. "Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data." Entropy 21, no. 2 (February 15, 2019): 184. http://dx.doi.org/10.3390/e21020184.

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Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. Recently, as deep learning models have become more common, RNNs have been used to forecast increasingly complicated systems. Dynamical spatio-temporal processes represent a class of complex systems that can potentially benefit from these types of models. Although the RNN literature is expansive and highly developed, uncertainty quantification is often ignored. Even when considered, the uncertainty is generally quantified without the use of a rigorous framework, such as a fully Bayesian setting. Here we attempt to quantify uncertainty in a more formal framework while maintaining the forecast accuracy that makes these models appealing, by presenting a Bayesian RNN model for nonlinear spatio-temporal forecasting. Additionally, we make simple modifications to the basic RNN to help accommodate the unique nature of nonlinear spatio-temporal data. The proposed model is applied to a Lorenz simulation and two real-world nonlinear spatio-temporal forecasting applications.

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Guo, Lingzhong, and Stephen A. Billings. "State-Space Reconstruction and Spatio-Temporal Prediction of Lattice Dynamical Systems." IEEE Transactions on Automatic Control 52, no. 4 (April 2007): 622–32. http://dx.doi.org/10.1109/tac.2007.894513.

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ITOH, MAKOTO, and LEON O. CHUA. "OSCILLATIONS ON THE EDGE OF CHAOS VIA DISSIPATION AND DIFFUSION." International Journal of Bifurcation and Chaos 17, no. 05 (May 2007): 1531–73. http://dx.doi.org/10.1142/s0218127407018336.

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The primary purpose of this paper is to show that simple dissipation can bring about oscillations in certain kinds of asymptotically stable nonlinear dynamical systems; namely when the system is locally active where the dissipation is introduced. Furthermore, if these nonlinear dynamical systems are coupled with appropriate choice of diffusion coefficients, then the coupled system can exhibit spatio-temporal oscillations. The secondary purpose of this paper is to show that spatio-temporal oscillations can occur in spatially discrete reaction diffusion equations operating on the edge of chaos, provided the array size is sufficiently large.

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GUO, YUZHU, STEVE A. BILLINGS, and DANIEL COCA. "IDENTIFICATION OF n-STATE SPATIO-TEMPORAL DYNAMICAL SYSTEMS USING A POLYNOMIAL MODEL." International Journal of Bifurcation and Chaos 18, no. 07 (July 2008): 2049–57. http://dx.doi.org/10.1142/s0218127408021543.

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A multivariable polynomial model is introduced to describe n-state spatio-temporal systems. Based on this model, a new neighborhood detection and transition rules determination method is proposed. Simulation results illustrate that the new method performs well even when the patterns are corrupted by static and dynamical noise.

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Guo, L. Z., S. A. Billings, and H. L. Wei. "Estimation of spatial derivatives and identification of continuous spatio-temporal dynamical systems." International Journal of Control 79, no. 9 (September 2006): 1118–35. http://dx.doi.org/10.1080/00207170600804050.

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Guo, L., and S. A. Billings. "Identification of Partial Differential Equation Models for Continuous Spatio-Temporal Dynamical Systems." IEEE Transactions on Circuits and Systems II: Express Briefs 53, no. 8 (August 2006): 657–61. http://dx.doi.org/10.1109/tcsii.2006.876464.

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Guo, L. Z., S. A. Billings, and D. Coca. "Identification of multiscale spatio-temporal dynamical systems using a wavelet multiresolution analysis." International Journal of Systems Science 40, no. 11 (November 2009): 1115–26. http://dx.doi.org/10.1080/00207720902974694.

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Baier, Gerold, and Sven Sahle. "Spatio-temporal patterns with hyperchaotic dynamics in diffusively coupled biochemical oscillators." Discrete Dynamics in Nature and Society 1, no. 2 (1997): 161–67. http://dx.doi.org/10.1155/s1026022697000162.

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We present three examples how complex spatio-temporal patterns can be linked to hyperchaotic attractors in dynamical systems consisting of nonlinear biochemical oscillators coupled linearly with diffusion terms. The systems involved are: (a) a two-variable oscillator with two consecutive autocatalytic reactions derived from the Lotka–Volterra scheme; (b) a minimal two-variable oscillator with one first-order autocatalytic reaction; (c) a three-variable oscillator with first-order feedback lacking autocatalysis. The dynamics of a finite number of coupled biochemical oscillators may account for complex patterns in compartmentalized living systems like cells or tissue, and may be tested experimentally in coupled microreactors.

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Ipsen, M., F. Hynne, and P. G. Sørensen. "Amplitude Equations and Chemical Reaction–Diffusion Systems." International Journal of Bifurcation and Chaos 07, no. 07 (July 1997): 1539–54. http://dx.doi.org/10.1142/s0218127497001217.

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The paper discusses the use of amplitude equations to describe the spatio-temporal dynamics of a chemical reaction–diffusion system based on an Oregonator model of the Belousov–Zhabotinsky reaction. Sufficiently close to a supercritical Hopf bifurcation the reaction–diffusion equation can be approximated by a complex Ginzburg–Landau equation with parameters determined by the original equation at the point of operation considered. We illustrate the validity of this reduction by comparing numerical spiral wave solutions to the Oregonator reaction–diffusion equation with the corresponding solutions to the complex Ginzburg–Landau equation at finite distances from the bifurcation point. We also compare the solutions at a bifurcation point where the systems develop spatio-temporal chaos. We show that the complex Ginzburg–Landau equation represents the dynamical behavior of the reaction–diffusion equation remarkably well, sufficiently far from the bifurcation point for experimental applications to be feasible.

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PALACIOS, ANTONIO, PETER BLOMGREN, and SCOTT GASNER. "BIFURCATION ANALYSIS OF HOPPING BEHAVIOR IN CELLULAR PATTERN-FORMING SYSTEMS." International Journal of Bifurcation and Chaos 17, no. 02 (February 2007): 509–20. http://dx.doi.org/10.1142/s0218127407017380.

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We use symmetry-based arguments to derive normal form equations for studying the temporal behavior of a particular spatio-temporal dynamic cellular pattern, called "hopping" state, which we have recently discovered in computer simulations of a generic example of an extended, deterministic, pattern-forming system in a circular domain. Hopping states are characterized by cellular structures that sequentially make abrupt changes in their angular positions while they rotate, collectively, about the center of the circular domain. A mode decomposition analysis suggests that these patterns are created from the interaction of three steady-state modes. A bifurcation analysis of associated normal form equations, which govern the time-evolution of the steady-state modes, helps us quantify the complexity of hopping patterns. Conditions for their existence and their stability are also derived from the bifurcation analysis. The overall ideas and methods are generic, so they can be readily applied to study other type of spatio-temporal pattern-forming dynamical systems with similar symmetry properties.

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BURLAKOV, VICTOR M. "SPATIAL- AND SPATIO-TEMPORAL PATTERN FORMATION IN OPTICALLY DRIVEN DISCRETE SYSTEMS." International Journal of Modern Physics B 13, no. 07 (March 20, 1999): 791–805. http://dx.doi.org/10.1142/s0217979299000667.

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Dynamical coherent structure (pattern) formation in the Klein–Gordon lattice excited by periodic external field near the optical resonance is studied. It is shown that the patterns involve spatial or spatio-temporal modulation of particles vibration amplitude in the lattice and can be generated in rather broad region of excitation parameters. An influence of cubic anharmonicity in the lattice potential and that of random noise on the pattern formation is examined.

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Sulis, William. "Transients as the Basis for Information Flow in Complex Adaptive Systems." Entropy 21, no. 1 (January 20, 2019): 94. http://dx.doi.org/10.3390/e21010094.

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Information is the fundamental currency of naturally occurring complex adaptive systems, whether they are individual organisms or collective social insect colonies. Information appears to be more important than energy in determining the behavior of these systems. However, it is not the quantity of information but rather its salience or meaning which is significant. Salience is not, in general, associated with instantaneous events but rather with spatio-temporal transients of events. This requires a shift in theoretical focus from instantaneous states towards spatio-temporal transients as the proper object for studying information flow in naturally occurring complex adaptive systems. A primitive form of salience appears in simple complex systems models in the form of transient induced global response synchronization (TIGoRS). Sparse random samplings of spatio-temporal transients may induce stable collective responses from the system, establishing a stimulus–response relationship between the system and its environment, with the system parsing its environment into salient and non-salient stimuli. In the presence of TIGoRS, an embedded complex dynamical system becomes a primitive automaton, modeled as a Sulis machine.

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Lai, Ying-Cheng, and Raimond L. Winslow. "Extreme sensitive dependence on parameters and initial conditions in spatio-temporal chaotic dynamical systems." Physica D: Nonlinear Phenomena 74, no. 3-4 (July 1994): 353–71. http://dx.doi.org/10.1016/0167-2789(94)90200-3.

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Klyushina, E. S., Yu S. Krivosenko, and A. A. Pavlychev. "Spatio-Temporal Dynamical Systems in Inner-Shell Photoionization in Free Molecules, Clusters, and Solids." Journal of Mathematical Sciences 202, no. 6 (October 2, 2014): 835–48. http://dx.doi.org/10.1007/s10958-014-2080-z.

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Buitink, Joost, Lieke A. Melsen, James W. Kirchner, and Adriaan J. Teuling. "A distributed simple dynamical systems approach (dS2 v1.0) for computationally efficient hydrological modelling at high spatio-temporal resolution." Geoscientific Model Development 13, no. 12 (December 2, 2020): 6093–110. http://dx.doi.org/10.5194/gmd-13-6093-2020.

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Abstract. In this paper, we introduce a new numerically robust distributed rainfall–runoff model for computationally efficient simulation at high spatio-temporal resolution: the distributed simple dynamical systems (dS2) model. The model is based on the simple dynamical systems approach as proposed by Kirchner (2009), and the distributed implementation allows for spatial heterogeneity in the parameters and/or model forcing fields at high spatio-temporal resolution (for instance as derived from precipitation radar data). The concept is extended with snow and routing modules, where the latter transports water from each pixel to the catchment outlet. The sensitivity function, which links changes in storage to changes in discharge, is implemented by a new three-parameter equation that is able to represent the widely observed downward curvature in log–log space. The simplicity of the underlying concept allows the model to calculate discharge in a computationally efficient manner, even at high temporal and spatial resolution, while maintaining proven model performance. The model code is written in Python in order to be easily readable and adjustable while maintaining computational efficiency. Since this model has short runtimes, it allows for extended sensitivity and uncertainty studies with relatively low computational costs. A test application shows good and consistent model performance across scales ranging from 3 to over 1700 km2.

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Hart, Joseph D., Laurent Larger, Thomas E. Murphy, and Rajarshi Roy. "Delayed dynamical systems: networks, chimeras and reservoir computing." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2153 (July 22, 2019): 20180123. http://dx.doi.org/10.1098/rsta.2018.0123.

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We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics, extensive research on optoelectronic feedback loops has revealed their immense potential for realizing complex system dynamics such as chimeras in rings of coupled oscillators and applications to reservoir computing. Delayed dynamical systems have been enriched in recent years through the application of digital signal processing techniques. Very recently, we have showed that one can significantly extend the capabilities and implement networks with arbitrary topologies through the use of field programmable gate arrays. This architecture allows the design of appropriate filters and multiple time delays, and greatly extends the possibilities for exploring synchronization patterns in arbitrary network topologies. This has enabled us to explore complex dynamics on networks with nodes that can be perfectly identical, introduce parameter heterogeneities and multiple time delays, as well as change network topologies to control the formation and evolution of patterns of synchrony. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

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Guo, L. Z., S. A. Billings, and D. Coca. "Identification of partial differential equation models for a class of multiscale spatio-temporal dynamical systems." International Journal of Control 83, no. 1 (August 3, 2009): 40–48. http://dx.doi.org/10.1080/00207170903085597.

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Guo, L. Z., S. S. Mei, and S. A. Billings. "Neighbourhood detection and identification of spatio-temporal dynamical systems using a coarse-to-fine approach." International Journal of Systems Science 38, no. 1 (January 2007): 1–15. http://dx.doi.org/10.1080/00207720600825339.

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Coulliette, C., and S. Wiggins. "Intergyre transport in a wind-driven, quasigeostrophic double gyre: An application of lobe dynamics." Nonlinear Processes in Geophysics 7, no. 1/2 (June 30, 2000): 59–85. http://dx.doi.org/10.5194/npg-7-59-2000.

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Abstract. We study the flow obtained from a three-layer, eddy-resolving quasigeostrophic ocean circulation model subject to an applied wind stress curl. For this model we will consider transport between the northern and southern gyres separated by an eastward jet. We will focus on the use of techniques from dynamical systems theory, particularly lobe dynamics, in the forming of geometric structures that govern transport. By "govern", we mean they can be used to compute Lagrangian transport quantities, such as the flux across the jet. We will consider periodic, quasiperiodic, and chaotic velocity fields, and thus assess the effectiveness of dynamical systems techniques in flows with progressively more spatio-temporal complexity. The numerical methods necessary to implement the dynamical systems techniques and the significance of lobe dynamics as a signature of specific "events", such as rings pinching off from a meandering jet, are also discussed.

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Coulliette, C., and S. Wiggins. "Intergyre transport in a wind-driven, quasigeostrophic double gyre: An application of lobe dynamics." Nonlinear Processes in Geophysics 8, no. 1/2 (April 30, 2001): 69–94. http://dx.doi.org/10.5194/npg-8-69-2001.

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Abstract. We study the flow obtained from a three-layer, eddy-resolving quasigeostrophic ocean circulation model subject to an applied wind stress curl. For this model we will consider transport between the northern and southern gyres separated by an eastward jet. We will focus on the use of techniques from dynamical systems theory, particularly lobe dynamics, in the forming of geometric structures that govern transport. By "govern", we mean they can be used to compute Lagrangian transport quantities, such as the flux across the jet. We will consider periodic, quasiperiodic, and chaotic velocity fields, and thus assess the effectiveness of dynamical systems techniques in flows with progressively more spatio-temporal complexity. The numerical methods necessary to implement the dynamical systems techniques and the significance of lobe dynamics as a signature of specific "events", such as rings pinching off from a meandering jet, are also discussed.

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Wilson, R. Eddie. "Mechanisms for spatio-temporal pattern formation in highway traffic models." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1872 (March 6, 2008): 2017–32. http://dx.doi.org/10.1098/rsta.2008.0018.

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A key qualitative requirement for highway traffic models is the ability to replicate a type of traffic jam popularly referred to as a phantom jam , shock wave or stop-and-go wave . Despite over 50 years of modelling, the precise mechanisms for the generation and propagation of stop-and-go waves and the associated spatio-temporal patterns are in dispute. However, the increasing availability of empirical datasets, such as those collected from motorway incident detection and automatic signalling system (MIDAS) inductance loops in the UK or the next-generation simulation trajectory data (NGSIM) project in the USA, means that we can expect to resolve these questions definitively in the next few years. This paper will survey the essence of the competing explanations of highway traffic pattern formation and introduce and analyse a new mechanism, based on dynamical systems theory and bistability, which can help resolve the conflict.

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KOZMA, ROBERT, MARKO PULJIC, and LEONID PERLOVSKY. "MODELING GOAL-ORIENTED DECISION MAKING THROUGH COGNITIVE PHASE TRANSITIONS." New Mathematics and Natural Computation 05, no. 01 (March 2009): 143–57. http://dx.doi.org/10.1142/s1793005709001246.

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Cognitive experiments indicate the presence of discontinuities in brain dynamics during high-level cognitive processing. Non-linear dynamic theory of brains pioneered by Freeman explains the experimental findings through the theory of metastability and edge-of-criticality in cognitive systems, which are key properties associated with robust operation and fast and reliable decision making. Recently, neuropercolation has been proposed to model such critical behavior. Neuropercolation is a family of probabilistic models based on the mathematical theory of bootstrap percolations on lattices and random graphs and motivated by structural and dynamical properties of neural populations in the cortex. Neuropercolation exhibits phase transitions and it provides a novel mathematical tool for studying spatio-temporal dynamics of multi-stable systems. The present work reviews the theory of cognitive phase transitions based on neuropercolation models and outlines the implications to decision making in brains and in artificial designs.

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Grace, Miriam, and Marc-Thorsten Hütt. "Predictability of spatio-temporal patterns in a lattice of coupled FitzHugh–Nagumo oscillators." Journal of The Royal Society Interface 10, no. 81 (April 6, 2013): 20121016. http://dx.doi.org/10.1098/rsif.2012.1016.

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In many biological systems, variability of the components can be expected to outrank statistical fluctuations in the shaping of self-organized patterns. In pioneering work in the late 1990s, it was hypothesized that a drift of cellular parameters (along a ‘developmental path’), together with differences in cell properties (‘desynchronization’ of cells on the developmental path) can establish self-organized spatio-temporal patterns (in their example, spiral waves of cAMP in a colony of Dictyostelium discoideum cells) starting from a homogeneous state. Here, we embed a generic model of an excitable medium, a lattice of diffusively coupled FitzHugh–Nagumo oscillators, into a developmental-path framework. In this minimal model of spiral wave generation, we can now study the predictability of spatio-temporal patterns from cell properties as a function of desynchronization (or ‘spread’) of cells along the developmental path and the drift speed of cell properties on the path. As a function of drift speed and desynchronization, we observe systematically different routes towards fully established patterns, as well as strikingly different correlations between cell properties and pattern features. We show that the predictability of spatio-temporal patterns from cell properties contains important information on the pattern formation process as well as on the underlying dynamical system.

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SANCHEZ, JUAN R. "MULTIFRACTAL CHARACTERISTICS OF LINEAR ONE-DIMENSIONAL CELLULAR AUTOMATA." International Journal of Modern Physics C 14, no. 04 (May 2003): 491–99. http://dx.doi.org/10.1142/s0129183103004681.

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Cellular automata (CA) can be considered as discrete dynamical systems exhibiting a rich intrinsic behavior both in space and time. Starting from disordered initial configurations and according to different local evolution rules, CA can evolve into steady states showing regular or complex space–time structures. These structures have been shown to have fractal and multifractal properties. Here, the multifractal properties of linear one-dimensional cellular automata with complex spatio-temporal behaviors are calculated using discrete wavelets transforms.

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Malchow, H., and N. Shigesada. "Nonequilibrium plankton community structures in an ecohydrodynamic model system." Nonlinear Processes in Geophysics 1, no. 1 (March 31, 1994): 3–11. http://dx.doi.org/10.5194/npg-1-3-1994.

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Abstract. Due to the local and global impacts of algae blooms and patchiness on water quality, carbon cycling and climate, models of plankton dynamics are of current interest. In this paper, the temporal and spatial patterns in natural plankton communities are interpreted as transient and stationary nonequilibrium solutions of dynamical nonlinear interaction-diffusion-advection systems. A simple model of phytoplankton-zooplankton dynamics (Scheffer, 1991) is presented in space and time. After summarizing the local properties as multiple stability and oscillations, the emergence of spatial and spatio- temporal patterns is considered, accounting also for diffusion and weak advection. In order to study the emergence and stability of these structures under hydrodynamic forcing, the interaction- diffusion-advection model is coupled to the hydrodynamic equations. It is shown, that the formation of nonequilibrium spatio-temporal density patterns due to the interplay of the deterministic nonlinear biological interactions and physical processes is a rare occurrence in rapidly flowing waters. The two-timing perturbation technique is applied to problems with very rapid single-directed steady flows. A channel under tidal forcing serves as and example for a system with a relatively high detention time of matter. Generally, due to the different time and length scales of planktic interactions, diffusion and transport, initial nonequilibrium plankton patches are simply moved through the system unless the strong hydrodynamic forces do not destroy them before.

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Expert, Paul, Renaud Lambiotte, Dante R. Chialvo, Kim Christensen, Henrik Jeldtoft Jensen, David J. Sharp, and Federico Turkheimer. "Self-similar correlation function in brain resting-state functional magnetic resonance imaging." Journal of The Royal Society Interface 8, no. 57 (September 22, 2010): 472–79. http://dx.doi.org/10.1098/rsif.2010.0416.

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Adaptive behaviour, cognition and emotion are the result of a bewildering variety of brain spatio-temporal activity patterns. An important problem in neuroscience is to understand the mechanism by which the human brain's 100 billion neurons and 100 trillion synapses manage to produce this large repertoire of cortical configurations in a flexible manner. In addition, it is recognized that temporal correlations across such configurations cannot be arbitrary, but they need to meet two conflicting demands: while diverse cortical areas should remain functionally segregated from each other, they must still perform as a collective, i.e. they are functionally integrated. Here, we investigate these large-scale dynamical properties by inspecting the character of the spatio-temporal correlations of brain resting-state activity. In physical systems, these correlations in space and time are captured by measuring the correlation coefficient between a signal recorded at two different points in space at two different times. We show that this two-point correlation function extracted from resting-state functional magnetic resonance imaging data exhibits self-similarity in space and time. In space, self-similarity is revealed by considering three successive spatial coarse-graining steps while in time it is revealed by the 1/ f frequency behaviour of the power spectrum. The uncovered dynamical self-similarity implies that the brain is spontaneously at a continuously changing (in space and time) intermediate state between two extremes, one of excessive cortical integration and the other of complete segregation. This dynamical property may be seen as an important marker of brain well-being in both health and disease.

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Ning, Hanwen, and Xingjian Jing. "Identification of partially known non-linear stochastic spatio-temporal dynamical systems by using a novel partially linear Kernel method." IET Control Theory & Applications 9, no. 1 (January 2, 2015): 21–33. http://dx.doi.org/10.1049/iet-cta.2014.0242.

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Lakshmanan, M. "The fascinating world of the Landau–Lifshitz–Gilbert equation: an overview." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1939 (March 28, 2011): 1280–300. http://dx.doi.org/10.1098/rsta.2010.0319.

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The Landau–Lifshitz–Gilbert (LLG) equation is a fascinating nonlinear evolution equation both from mathematical and physical points of view. It is related to the dynamics of several important physical systems such as ferromagnets, vortex filaments, moving space curves, etc. and has intimate connections with many of the well-known integrable soliton equations, including nonlinear Schrödinger and sine-Gordon equations. It can admit very many dynamical structures including spin waves, elliptic function waves, solitons, dromions, vortices, spatio-temporal patterns, chaos, etc. depending on the physical and spin dimensions and the nature of interactions. An exciting recent development is that the spin torque effect in nanoferromagnets is described by a generalization of the LLG equation that forms a basic dynamical equation in the field of spintronics. This article will briefly review these developments as a tribute to Robin Bullough who was a great admirer of the LLG equation.

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Fronzoni, Leone, and Michele Giocondo. "Controlling Chaos with Parametric Perturbations." International Journal of Bifurcation and Chaos 08, no. 08 (August 1998): 1693–98. http://dx.doi.org/10.1142/s0218127498001364.

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We consider the effects of parametric perturbation on the onset of chaos in different dynamical systems. Favoring or suppression of chaos was observed depending on the phase or the frequency of the periodic perturbation. A lowering of the threshold of chaos was observed in an electronic device simulating a Josephson-Junction model and the suppression of chaos was obtained in a bistable mechanical device. We showed that in case of spatial instability in a sample of liquid crystal, the action of the parametric perturbation is to modify the velocity and the onset of the defects. Considering that the emergence of defects precedes the threshold of spatio-temporal chaos, we infer that parametric perturbation can modify the threshold of chaos in this spatial dynamical system.

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Ortega, Juan-Pablo. "Relative normal modes for nonlinear Hamiltonian systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 133, no. 3 (June 2003): 665–704. http://dx.doi.org/10.1017/s0308210500002602.

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An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework of a classical result by Weinstein and Moser on the existence of periodic orbits in the energy levels surrounding a stable equilibrium. The estimate obtained is very precise in the sense that it provides a lower bound for the number of relative periodic orbits at each prescribed energy and momentum values neighbouring the stable relative equilibrium in question and with any prefixed (spatio-temporal) isotropy subgroup. Moreover, it is easily computable in particular examples. It is interesting to see how, in our result, the existence of non-trivial relative periodic orbits requires (generic) conditions on the higher-order terms of the Taylor expansion of the Hamiltonian function, in contrast with the purely quadratic requirements of the Weinstein–Moser theorem, which emphasizes the highly nonlinear character of the relatively periodic dynamical objects.

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Goldbeter, Albert. "Dissipative structures in biological systems: bistability, oscillations, spatial patterns and waves." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2124 (June 11, 2018): 20170376. http://dx.doi.org/10.1098/rsta.2017.0376.

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The goal of this review article is to assess how relevant is the concept of dissipative structure for understanding the dynamical bases of non-equilibrium self-organization in biological systems, and to see where it has been applied in the five decades since it was initially proposed by Ilya Prigogine. Dissipative structures can be classified into four types, which will be considered, in turn, and illustrated by biological examples: (i) multistability, in the form of bistability and tristability, which involve the coexistence of two or three stable steady states, or in the form of birhythmicity, which involves the coexistence between two stable rhythms; (ii) temporal dissipative structures in the form of sustained oscillations, illustrated by biological rhythms; (iii) spatial dissipative structures, known as Turing patterns; and (iv) spatio-temporal structures in the form of propagating waves. Rhythms occur with widely different periods at all levels of biological organization, from neural, cardiac and metabolic oscillations to circadian clocks and the cell cycle; they play key roles in physiology and in many disorders. New rhythms are being uncovered while artificial ones are produced by synthetic biology. Rhythms provide the richest source of examples of dissipative structures in biological systems. Bistability has been observed experimentally, but has primarily been investigated in theoretical models in an increasingly wide range of biological contexts, from the genetic to the cell and animal population levels, both in physiological conditions and in disease. Bistable transitions have been implicated in the progression between the different phases of the cell cycle and, more generally, in the process of cell fate specification in the developing embryo. Turing patterns are exemplified by the formation of some periodic structures in the course of development and by skin stripe patterns in animals. Spatio-temporal patterns in the form of propagating waves are observed within cells as well as in intercellular communication. This review illustrates how dissipative structures of all sorts abound in biological systems. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)’.

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Nwokoye, ChukwuNonso, and Ikechukwu Umeh. "Analytic-agent cyber dynamical systems analysis and design method for modeling spatio-temporal factors of malware propagation in wireless sensor networks." MethodsX 5 (2018): 1373–98. http://dx.doi.org/10.1016/j.mex.2018.10.005.

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MUEZZINOGLU, MEHMET K., IRMA TRISTAN, RAMON HUERTA, VALENTIN S. AFRAIMOVICH, and MIKHAIL I. RABINOVICH. "TRANSIENTS VERSUS ATTRACTORS IN COMPLEX NETWORKS." International Journal of Bifurcation and Chaos 20, no. 06 (June 2010): 1653–75. http://dx.doi.org/10.1142/s0218127410026745.

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Understanding and predicting the behavior of complex multiagent systems like brain or ecological food net requires new approaches and paradigms. Traditional analyses based on just asymptotic results of behavior as time goes to infinity, or on straightforward mathematical images that can accommodate only fixed points or limit cycles do not tell much about these systems. To obtain sensible dynamical models of natural phenomena, such as the reproducible order observed in ecological, cognitive or behavioral experiments, one cannot afford to neglect the transient dynamics of the underlying complex network. In disclosing such dynamical mechanisms, the focus of interest must be on reproducible or, even, structurally stable transients. In this tutorial, we formulate the Winnerless Competition (WLC) principle that induces robust transient dynamics in open complex networks. The main point of WLC principle is the transformation of the acquired information into ensemble (spatio)-temporal output via intrinsic transient dynamics of the network. Such encoding provides a reproducible transient response, whose geometrical image in phase space is a stable heteroclinic sequence. We compile a diverse list of natural phenomena which can be rigorously modeled by the WLC. Together with the experimental and numerical results of the networks with different levels of complexity, we evaluate the robustness and reproducibility of the WLC dynamics and discuss the advantages of future possible application of the discussed approach.

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García-Garrido, V. J., A. M. Mancho, S. Wiggins, and C. Mendoza. "A dynamical systems perspective on the absence of debris associated with the disappearance of flight MH370." Nonlinear Processes in Geophysics Discussions 2, no. 4 (July 27, 2015): 1197–225. http://dx.doi.org/10.5194/npgd-2-1197-2015.

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Abstract. The disappearance of Malaysia Airlines flight MH370 on the morning of the 8 March 2014 is one of the great mysteries of our time. Perhaps the most relevant aspect of this mystery is that not a single piece of debris from the aircraft has been found. Difficulties in the search efforts, due to the uncertainty in the plane's final impact point and the time that has passed since the accident, bring the question on how the debris has scattered in an always moving ocean, for which there are multiple data sets that do not uniquely determine its state. Our approach to this problem is based on the use of Lagrangian Descriptors (LD), a novel mathematical tool coming from dynamical systems theory that identifies dynamic barriers and coherent structures governing transport. By combining publicly available information supplied by different ocean data sources with these mathematical techniques, we are able to assess the spatio-temporal state of the ocean in the priority search area at the time of impact and the following weeks. Using this information we propose a revised search strategy by showing why one might not have expected to find debris in some large search areas targeted by the Australian Maritime Safety Authority (AMSA), and determining regions where one might have expected impact debris to be located and that have not been subjected to any exploration.

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Kuske, R., and D. Yurchenko. "Editorial." European Journal of Applied Mathematics 30, no. 5 (September 9, 2019): 829. http://dx.doi.org/10.1017/s0956792518000694.

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The origin of this special issue took place at the 9th European Nonlinear Dynamics Conference (ENOC 2017) in Budapest, Hungary. Specifically, the mini-symposium on Random Dynamical Systems – Recent Advances and New Directions brought together novel perspectives on analyzing stochastic dynamics with applications including biology, structural dynamics, control, energy and mechanics. The expanded use of stochasticity in more realistic models exposes questions related to bifurcations, meta-stability, tipping and early warning signals, multiscale dynamics, and connections between chaos and stochastic dynamics. The observed phenomena in applications drive new methodologies and analyses, needed to understand the interplay between different sources of stochastic effects and nonlinearities, network structure, multi-mode and multi-scale behavior, non-smooth dynamics, energy transfer, and spatio-temporal phenomena. Of course, a single issue cannot hope to cover all of the new topics in stochastic analysis for applications. Nevertheless, we hope that the collection of applications and stochastic models presented in this issue illustrates some of the exciting advances and perspectives relevant for broad classes of stochastic models and demonstrates the need in advancing the theory of stochastic processes.

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Willis, Gary, and Gunnar Pruessner. "Spatio-temporal correlations in the Manna model in one, three and five dimensions." International Journal of Modern Physics B 32, no. 05 (February 2018): 1830002. http://dx.doi.org/10.1142/s0217979218300025.

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Although the paradigm of criticality is centered around spatial correlations and their anomalous scaling, not many studies of self-organized criticality (SOC) focus on spatial correlations. Often, integrated observables, such as avalanche size and duration, are used, not least as to avoid complications due to the unavoidable lack of translational invariance. The present work is a survey of spatio-temporal correlation functions in the Manna Model of SOC, measured numerically in detail in [Formula: see text] = 1,3 and 5 dimensions and compared to theoretical results, in particular relating them to “integrated” observables such as avalanche size and duration scaling, that measure them indirectly. Contrary to the notion held by some of SOC models organizing into a critical state by re-arranging their spatial structure avalanche by avalanche, which may be expected to result in large, nontrivial, system-spanning spatial correlations in the quiescent state (between avalanches), correlations of inactive particles in the quiescent state have a small amplitude that does not and cannot increase with the system size, although they display (noisy) power law scaling over a range linear in the system size. Self-organization, however, does take place as the (one-point) density of inactive particles organizes into a particular profile that is asymptotically independent of the driving location, also demonstrated analytically in one dimension. Activity and its correlations, on the other hand, display nontrivial long-ranged spatio-temporal scaling with exponents that can be related to established results, in particular avalanche size and duration exponents. The correlation length and amplitude are set by the system size (confirmed analytically for some observables), as expected in systems displaying finite size scaling. In one dimension, we find some surprising inconsistencies of the dynamical exponent. A (spatially extended) mean field theory (MFT) is recovered, with some corrections, in five dimensions.

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García-Garrido, V. J., A. M. Mancho, S. Wiggins, and C. Mendoza. "A dynamical systems approach to the surface search for debris associated with the disappearance of flight MH370." Nonlinear Processes in Geophysics 22, no. 6 (November 25, 2015): 701–12. http://dx.doi.org/10.5194/npg-22-701-2015.

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Abstract. The disappearance of Malaysia Airlines flight MH370 on the morning of 8 March 2014 is one of the great mysteries of our time. Perhaps the most relevant aspect of this mystery is that not a single piece of debris from the aircraft was found during the intensive surface search carried out for roughly 2 months following the crash. Difficulties in the search efforts, due to the uncertainty of the plane's final impact point and the time that had passed since the accident, bring the question on how the debris scattered in an always moving ocean, for which there are multiple data sets that do not uniquely determine its state. Our approach to this problem is based on the use of Lagrangian descriptors (LD), a novel mathematical tool coming from dynamical systems theory that identifies dynamic barriers and coherent structures governing transport. By combining publicly available information supplied by different ocean data sources with these mathematical techniques, we are able to assess the spatio-temporal state of the ocean in the priority search area at the time of impact and the following weeks. Using this information we propose a revised search strategy by showing why one might not have expected to find debris in some large search areas targeted by the Australian Maritime Safety Authority (AMSA), and determining regions where one might have expected impact debris to be located, which were not subjected to any exploration.

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KOZMA, ROBERT, and H. JOHN CAULFIELD. "NEURODYNAMIC CORRELATES OF HIGHER COGNITION AND CONSCIOUSNESS — EDITORIAL." New Mathematics and Natural Computation 05, no. 01 (March 2009): 1–6. http://dx.doi.org/10.1142/s1793005709001350.

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In spite of the explosive growth of experimental research in basic neurobiology and neurophysiology of brain components in the past decade, understanding the integrated functioning of the brain remains a significant scientific challenge. Essential for understanding human brain function is the detailed knowledge concerning the spatio-temporal dynamics of neuronal populations and their intricate interactions during cognitive functions. The aim of the present issue is to examine brain dynamics and cognitive functions from a multidisciplinary perspective and to introduce the most recent results in this research frontier. Topics relevant to the special issue include: (i) Modeling brain dynamics at the mesoscopic and macroscopic scales, including dynamical systems with distributed parameters; (ii) Applying tools of discrete mathematics, statistical and quantum physics, network science to describe the dynamics of brains; (iii) Experimental research on brain dynamics from various aspects, including fundamental neurobiology, evoked potentials, functional brain imaging, and cognitive functions; (iv) Clinical neuroscience issues for improved diagnosis of dynamic brain diseases and their potential therapies. This special issue is dedicated to Professor Walter J. Freeman on the occasion of his 80th birthday. Dr. Freeman produced breakthrough contributions to research on brain dynamics over the past five decades. The present issue covers all aspects of neurodynamics, starting from neural populations of high-level cognition and consciousness, as well as philosophical aspects and practical implementations on digital computers and hardware designs.

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CROUNSE, K. R., L. O. CHUA, P. THIRAN, and G. SETTI. "CHARACTERIZATION AND DYNAMICS OF PATTERN FORMATION IN CELLULAR NEURAL NETWORKS." International Journal of Bifurcation and Chaos 06, no. 09 (September 1996): 1703–24. http://dx.doi.org/10.1142/s0218127496001053.

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We study some properties of pattern formation arising in large arrays of locally coupled first-order nonlinear dynamical systems, namely Cellular Neural Networks (CNNs). We will present exact results to analyze spatial patterns for symmetric coupling and to analyze spatio-temporal patterns for anti-symmetric coupling in one-dimensional lattices, which will then be completed by approximative results based on a spatial and/or temporal frequency approach. We will discuss the validity of these approximations, which bring a lot of insight. This spectral approach becomes very convenient for the two-dimensional lattice, as exact results get more complicated to establish. In this second part, we will only consider a symmetric coupling between cells. We will show what kinds of motifs can be found in the patterns generated by 3×3 templates. Then, we will discuss the dynamics of pattern formation starting from initial conditions which are a small random noise added to the unstable equilibrium: this can generally be well predicted by the spatial frequency approach. We will also study whether a defect in a pure pattern can propagate or not through the whole lattice, starting from initial conditions being a localized perturbation of a stable pattern: this phenomenon is no longer correctly predicted by the spatial frequency approach. We also show that patterns such as spirals and targets can be formed by “seed” initial conditions — localized, non-random perturbations of an unstable equilibrium. Finally, the effects on the patterns formed of a bias term in the dynamics are demonstrated.

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Amoddeo, Antonino. "Modeling Avascular Tumor Growth: Approach with an Adaptive Grid Numerical Technique." Journal of Multiscale Modelling 09, no. 03 (September 2018): 1840002. http://dx.doi.org/10.1142/s1756973718400024.

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The mathematical modeling of complex biological systems leads to system of coupled nonlinear partial differential equations (PDEs). In this paper, we present a short review on the interaction of the urokinase plasminogen activator (uPA) system with a model for cancer cell in the avascular phase, faced using the moving mesh PDE/(MMPDE) numerical technique. The dynamical evolution of the system as a function of the diffusion properties of cancer cells has been considered, as well as the effect of hypoxia to the cancer evolution, introducing a model equation for the nutrient oxygen. The model parameters have been taken from the data existing in the literature, in particular to gauge the oxygen supply, data determined from in vivo experiments on human tumors have been used. The numerical results obtained simulating a one-dimensional portion of the biological tissue are consistent with the data existing in the literature. Our high-resolution computations show that cancer proliferation begins through highly irregular spatio-temporal pattern, which depends on cancer motility characteristics. In presence of hypoxia, the cancer proliferation patterns are still characterized by an inhomogeneous pattern, but other effects are present which depend on the model parameters, triggered by the oxygen.

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Sanghi, Sanjeev, and Nadine Aubry. "Mode interaction models for near-wall turbulence." Journal of Fluid Mechanics 247 (February 1993): 455–88. http://dx.doi.org/10.1017/s0022112093000527.

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Intermittent bursting events, similar to those characterizing the dynamics of near-wall turbulence, have been observed in a low-dimensional dynamical model (Aubry et al. 1988) built from eigenfunctions of the proper orthogonal decomposition (Lumley 1967). In the present work, we investigate the persistency of the intermittent behaviour in higher - but still of relatively low-dimensional dynamical systems. In particular, streamwise variations which were not accounted for in an explicit way in Aubry et al.'s model are now considered. Intermittent behaviour persists but can be of a different nature. Specifically, the non-zero streamwise modes become excited during the eruptive events so that rolls burst downstream into smaller scales. When structures have a finite length, they travel at a convection speed approximately equal to the mean velocity at the top of the layer (y+ ≈ 40). In all cases, intermittency seems to be due to homoclinic cycles connecting hyperbolic fixed points or more complex (apparently chaotic) limit sets. While these sets lie in the zero streamwise modes invariant subspace, the connecting orbits consist of nonzero streamwise modes travelling downstream. Chaotic limit sets connected by quasi-travelling waves have also been observed in a spatio-temporal chaotic regime of the Kuramoto–Sivashinsky equation (Aubry & Lian 1992a). When the limit sets lose their steadiness, the elongated rolls become randomly active, as they probably are in the real flow. A coherent structure study in our resulting flow fields is performed in order to relate our findings to experimental observations. It is shown that streaks, streamwise rolls, horseshoe vortical structures and shear layers, present in our models, are all connected to each other. Finally, criteria to determine a realistic value of the eddy viscosity parameter are developed.

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Doyon, Benjamin, and Jason Myers. "Fluctuations in Ballistic Transport from Euler Hydrodynamics." Annales Henri Poincaré 21, no. 1 (November 15, 2019): 255–302. http://dx.doi.org/10.1007/s00023-019-00860-w.

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AbstractWe propose a general formalism, within large-deviation theory, giving access to the exact statistics of fluctuations of ballistically transported conserved quantities in homogeneous, stationary states. The formalism is expected to apply to any system with an Euler hydrodynamic description, classical or quantum, integrable or not, in or out of equilibrium. We express the exact scaled cumulant generating function (or full counting statistics) for any (quasi-)local conserved quantity in terms of the flux Jacobian. We show that the “extended fluctuation relations” of Bernard and Doyon follow from the linearity of the hydrodynamic equations, forming a marker of “freeness” much like the absence of hydrodynamic diffusion does. We show how an extension of the formalism gives exact exponential behaviours of spatio-temporal two-point functions of twist fields, with applications to order-parameter dynamical correlations in arbitrary homogeneous, stationary state. We explain in what situations the large-deviation principle at the basis of the results fail, and discuss how this connects with nonlinear fluctuating hydrodynamics. Applying the formalism to conformal hydrodynamics, we evaluate the exact cumulants of energy transport in quantum critical systems of arbitrary dimension at low but nonzero temperatures, observing a phase transition for Lorentz boosts at the sound velocity.

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Klamser, Pascal P., and Pawel Romanczuk. "Collective predator evasion: Putting the criticality hypothesis to the test." PLOS Computational Biology 17, no. 3 (March 15, 2021): e1008832. http://dx.doi.org/10.1371/journal.pcbi.1008832.

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According to the criticality hypothesis, collective biological systems should operate in a special parameter region, close to so-called critical points, where the collective behavior undergoes a qualitative change between different dynamical regimes. Critical systems exhibit unique properties, which may benefit collective information processing such as maximal responsiveness to external stimuli. Besides neuronal and gene-regulatory networks, recent empirical data suggests that also animal collectives may be examples of self-organized critical systems. However, open questions about self-organization mechanisms in animal groups remain: Evolutionary adaptation towards a group-level optimum (group-level selection), implicitly assumed in the “criticality hypothesis”, appears in general not reasonable for fission-fusion groups composed of non-related individuals. Furthermore, previous theoretical work relies on non-spatial models, which ignore potentially important self-organization and spatial sorting effects. Using a generic, spatially-explicit model of schooling prey being attacked by a predator, we show first that schools operating at criticality perform best. However, this is not due to optimal response of the prey to the predator, as suggested by the “criticality hypothesis”, but rather due to the spatial structure of the prey school at criticality. Secondly, by investigating individual-level evolution, we show that strong spatial self-sorting effects at the critical point lead to strong selection gradients, and make it an evolutionary unstable state. Our results demonstrate the decisive role of spatio-temporal phenomena in collective behavior, and that individual-level selection is in general not a viable mechanism for self-tuning of unrelated animal groups towards criticality.

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Wolters, E. L. A., B. J. J. M. van den Hurk, and R. A. Roebeling. "Evaluation of rainfall retrievals from SEVIRI reflectances over West Africa using TRMM-PR and CMORPH." Hydrology and Earth System Sciences 15, no. 2 (February 3, 2011): 437–51. http://dx.doi.org/10.5194/hess-15-437-2011.

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Abstract. This paper describes the evaluation of the KNMI Cloud Physical Properties – Precipitation Properties (CPP-PP) algorithm over West Africa. The algorithm combines condensed water path (CWP), cloud phase (CPH), cloud particle effective radius (re), and cloud-top temperature (CTT) retrievals from visible, near-infrared and thermal infrared observations of the Spinning Enhanced Visible and Infrared Imager (SEVIRI) onboard the Meteosat Second Generation (MSG) satellites to estimate rain occurrence frequency and rain rate. For the 2005 and 2006 monsoon seasons, it is investigated whether the CPP-PP algorithm is capable of retrieving rain occurrence frequency and rain rate over West Africa with sufficient accuracy, using Tropical Monsoon Measurement Mission Precipitation Radar (TRMM-PR) as reference. As a second goal, it is assessed whether SEVIRI is capable of monitoring the seasonal and daytime evolution of rainfall during the West African monsoon (WAM), using Climate Prediction Center Morphing Technique (CMORPH) rainfall observations. The SEVIRI-detected rainfall area agrees well with TRMM-PR, with the areal extent of rainfall by SEVIRI being ~10% larger than from TRMM-PR. The mean retrieved rain rate from CPP-PP is about 8% higher than from TRMM-PR. Examination of the TRMM-PR and CPP-PP cumulative frequency distributions revealed that differences between CPP-PP and TRMM-PR are generally within +/−10%. Relative to the AMMA rain gauge observations, CPP-PP shows very good agreement up to 5 mm h−1. However, at higher rain rates (5–16 mm h−1) CPP-PP overestimates compared to the rain gauges. With respect to the second goal of this paper, it was shown that both the accumulated precipitation and the seasonal progression of rainfall throughout the WAM is in good agreement with CMORPH, although CPP-PP retrieves higher amounts in the coastal region of West Africa. Using latitudinal Hovmüller diagrams, a fair correspondence between CPP-PP and CMORPH was found, which is reflected by high correlation coefficients (~0.7) for both rain rate and rain occurrence frequency. The daytime cycle of rainfall from CPP-PP shows distinctly different patterns for three different regions in West Africa throughout the WAM, with a decrease in dynamical range of rainfall near the Inter Tropical Convergence Zone (ITCZ). The dynamical range as retrieved from CPP-PP is larger than that from CMORPH. It is suggested that this results from both the better spatio-temporal resolution of SEVIRI, as well as from thermal infrared radiances being partly used by CMORPH, which likely smoothes the daytime precipitation signal, especially in case of cold anvils from convective systems. The promising results show that the CPP-PP algorithm, taking advantage of the high spatio-temporal resolution of SEVIRI, is of added value for monitoring daytime precipitation patterns in tropical areas.

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Lorente, Pablo, Marcos García-Sotillo, Arancha Amo-Baladrón, Roland Aznar, Bruno Levier, José C. Sánchez-Garrido, Simone Sammartino, et al. "Skill assessment of global, regional, and coastal circulation forecast models: evaluating the benefits of dynamical downscaling in IBI (Iberia–Biscay–Ireland) surface waters." Ocean Science 15, no. 4 (July 22, 2019): 967–96. http://dx.doi.org/10.5194/os-15-967-2019.

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Abstract. In this work, a multi-parameter inter-comparison of diverse ocean forecast models was conducted at the sea surface ranging from global to local scales in a two-phase stepwise strategy. Firstly, a comparison of CMEMS GLOBAL and the nested CMEMS IBI regional system was performed against satellite-derived and in situ observations. Results highlighted the overall benefits of both the GLOBAL direct data assimilation in open water and the increased horizontal resolution of IBI in coastal areas. Besides, IBI (Iberia–Biscay–Ireland) proved to capture shelf dynamics by better representing the horizontal extent and strength of a river freshwater plume, according to the results derived from the validation against in situ observations from a buoy moored in NW Spain. Secondly, a multi-model inter-comparison exercise for 2017 was performed in the Strait of Gibraltar among GLOBAL, IBI, and SAMPA (Sánchez-Garrido et al., 2013) high-resolution coastal forecast systems (partially nested to IBI) in order to elucidate the accuracy of each system to characterize the Atlantic Jet (AJ) inflow dynamics. A quantitative validation against hourly currents from high-frequency radar (HFR) highlighted both the steady improvement in AJ representation in terms of speed and direction when zooming from global to coastal scales through a multi-nesting model approach and also the relevance of a variety of factors at local scale such as a refined horizontal resolution, a tailored bathymetry, and a higher spatio-temporal resolution of the atmospheric forcing. The ability of each model to reproduce a 2 d quasi-permanent full reversal of the AJ surface inflow was examined in terms of wind-induced circulation patterns. SAMPA appeared to better reproduce the reversal events detected with HFR estimations, demonstrating the added value of imposing accurate meteorologically driven barotropic velocities in the open boundaries (imported from the NIVMAR (Álvarez-Fanjul et al., 2001) storm surge model) to take into account the remote effect of the atmospheric forcing over the entire Mediterranean basin, which was only partially included in IBI and GLOBAL systems. Finally, SAMPA coastal model outputs were also qualitatively analysed in the western Alboran Sea to put in a broader perspective the context of the onset, development, and end of such flow reversal episodes.

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Journal articles on the topic 'Spatio-temporal dynamical systems'

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