### Dynamical systems

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An unresolved problem in neuroscience is to determine the relevant timescale for understanding spatiotemporal dynamics of the brain. Here, the authors introduce a new framework to study the different timescales through binning the output of a generative model of neural activity. Article 15 January Open Access. To explain the neural correlates of behavior and its variability, one must analyze single-trial population dynamics. Here, the authors develop a statistical method that extracts low-dimensional dynamics that explain behavior better than high-dimensional neural activity revealing unexpected structure.

Article 17 December Open Access.

## Planar Dynamical Systems : Selected Classical Problems

Noisy gene expression leading to phenotypic variability can help organisms to survive in changing environments. Here, Patange et al. Article 23 August Open Access. Causality inference in time series analysis based on temporal precedence principle between cause and effect fails to detect mutual causal interactions.

Here, Yang et al. Article 30 July Open Access. Coordination of neural activity between distant brain areas is necessary for cognition. Article 27 June Open Access. Brain activity is driven, in part, by external stimuli and demands, but internal brain states also change over time. Here, the authors use a novel Bayesian algorithm to track dynamic transitions between hidden neural states in human brain activity and to relate brain dynamics with behavior.

Article 14 March Open Access. A major goal of epilepsy research is understanding the spatiotemporal dynamics of seizure.

### Poisson-Gamma dynamical systems

Here, the authors extend the Epileptor neural mass model into a neural field model, in order to provide a unified and patient-specific model of seizure initiation, propagation, and termination. Article 20 December Open Access. FORCE training is a. Here the authors implement FORCE training in models of spiking neuronal networks and demonstrate that these networks can be trained to exhibit different dynamic behaviours.

## Dynamical Systems by Example | Luís Barreira | Springer

Article 12 December Open Access. Though the amplitude and frequency of neural oscillations in the alpha band are related to dissociable visual processes, they are not independent mathematically. Here, the authors show that fluctuations in instantaneous frequency predict alpha amplitude during visual discrimination tasks. Article 17 November Open Access.

Cybergenetics aims to monitor and regulate cellular processes in real-time using computer monitoring and feedback of biological readouts. Here the authors use a feedback loop and periodic forcing to maintain cells with a bistable synthetic circuit near its unstable state. Article 21 September Open Access. Active locomotion requires closed-loop sensorimotor co ordination between perception and action. Here the authors show using behavioural, imaging and modelling approaches that gaze orientation during phototaxis behaviour in larval zebrafish is related to oscillatory dynamics of a neuronal population in the hindbrain.

Article 09 August Open Access. Focal cortical seizures result from local and widespread propagation of excitatory activity. Here the authors employ widefield calcium imaging in mouse visual areas to demonstrate that these seizures start as local synchronous activation and then propagate along the connectivity that underlies normal sensory processing. Article 18 July Open Access. The influence of insulin on food preference and the corresponding underlying neural circuits are unknown in humans. Here, the authors show that increasing insulin changes food preference by modulating mesolimbic neural circuits, and that this pattern is changed in insulin-resistant individuals.

Article 11 April Open Access. Protein RNA interactions are dynamic and regulated in response to environmental changes. Article 04 October Open Access. Modelling of chaos and oscillations is usually done indirectly and quantitatively by fitting models to a finite number of data-points. Here, a qualitative framework is developed where the characteristics of the underlying dynamical system are directly specified, revealing new properties of such systems. Article 13 September Open Access.

## Quantum Dynamical Systems

The paradigm of reservoir computing shows that, like the human brain, complex networks can perform efficient information processing. Here, a simple delay dynamical system is demonstrated that can efficiently perform computations capable of replacing a complex network in reservoir computing. Advanced search. Skip to main content. Article 03 September Open Access Propagation of temporal and rate signals in cultured multilayer networks The nature of the signals that propagate through feedforward networks is not well understood.

This article is about the general aspects of dynamical systems. For technical details, see Dynamical system definition. For the study, see Dynamical systems theory. For other uses, see Dynamical disambiguation.

Main article: Dynamical system definition. Main article: Linear dynamical system. Main article: Bifurcation theory. Main article: Ergodic theory. Main article: Chaos theory. Main article: Measure-preserving dynamical system. Systems science portal. Behavioral modeling Cognitive modeling Complex dynamics Dynamic approach to second language development Dynamical systems theory Feedback passivation Infinite compositions of analytic functions List of dynamical system topics Oscillation People in systems and control Sharkovskii's theorem System dynamics Systems theory Principle of maximum caliber.

Introduction to the Modern Theory of Dynamical Systems. Cambridge: Cambridge University Press. Springer Nature.

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Retrieved 17 February Bibcode : Chaos.. Bibcode : JSP Applications of Dynamical Systems in Biology and Medicine. Advanced Engineering Mathematics. Hoboken: Wiley. Economic Dynamics: Methods and Models Fourth ed. Berlin: Springer. Works providing a broad coverage: Ralph Abraham and Jerrold E. Marsden Foundations of mechanics. Christian Bonatti; Lorenzo J. Stephen Smale Bulletin of the American Mathematical Society. Introductory texts with a unique perspective: V. Arnold Mathematical methods of classical mechanics.

Jacob Palis and Welington de Melo Geometric theory of dynamical systems: an introduction. David Ruelle Elements of Differentiable Dynamics and Bifurcation Theory. Academic Press. Ergodic theory, symbolic dynamics and hyperbolic spaces. Oxford University Press. CS1 maint: multiple names: authors list link Ralph H. Abraham and Christopher D. Shaw Dynamics—the geometry of behavior, 2nd edition. Textbooks Kathleen T. Alligood, Tim D. Sauer and James A. Yorke An introduction to dynamical systems. Springer Verlag. Oded Galor Discrete Dynamical Systems.

Morris W. Hirsch , Stephen Smale and Robert L. Devaney Differential Equations, dynamical systems, and an introduction to chaos. Anatole Katok; Boris Hasselblatt Introduction to the modern theory of dynamical systems. Stephen Lynch Dynamical Systems with Applications using Maple 2nd Ed. Springer International Publishing. Dynamical Systems with Applications using Mathematica 2nd Ed. Dynamical Systems with Applications using Python. James Meiss Differential Dynamical Systems.

David D. Nolte Julien Clinton Sprott Chaos and time-series analysis. Steven H. Strogatz Nonlinear dynamics and chaos: with applications to physics, biology chemistry and engineering. Addison Wesley. Teschl, Gerald Ordinary Differential Equations and Dynamical Systems. Providence : American Mathematical Society. Stephen Wiggins Introduction to Applied Dynamical Systems and Chaos. Popularizations: Florin Diacu and Philip Holmes Celestial Encounters. James Gleick Chaos: Making a New Science.

Ivar Ekeland Mathematics and the Unexpected Paperback. University Of Chicago Press. Ian Stewart Does God Play Dice? The New Mathematics of Chaos. Systems science. Doubling time Leverage points Limiting factor Negative feedback Positive feedback. Alexander Bogdanov Russell L. Hall Lydia Kavraki James J. Kay Faina M. Systems theory in anthropology Systems theory in archaeology Systems theory in political science. List Principia Cybernetica. Category Portal Commons. Chaos theory. Yorke Lai-Sang Young.

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