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Robustness and reproducibility of sequential spatio-temporal responses is an essential feature of many neural circuits in sensory and motor systems of animals. The most common mathematical images of dynamical regimes in neural systems are fixed points, limit cycles, chaotic attractors, and continuous attractors (attractive manifolds of neutrally stable… (More)

- Mikhail I. Rabinovich, Ramón Huerta, Pablo Varona, Valentin S. Afraimovich
- PLoS Computational Biology
- 2008

The idea that cognitive activity can be understood using nonlinear dynamics has been intensively discussed at length for the last 15 years. One of the popular points of view is that metastable states play a key role in the execution of cognitive functions. Experimental and modeling studies suggest that most of these functions are the result of transient… (More)

- Valentin S. Afraimovich, Mikhail I. Rabinovich, Pablo Varona
- I. J. Bifurcation and Chaos
- 2004

The ability of nonlinear dynamical systems to process incoming information is a key problem of many fundamental and applied sciences. Information processing by computation with attractors (steady states, limit cycles and strange attractors) has been a subject of many publications. In this paper we discuss a new direction in information dynamics based on… (More)

Predicting the evolution of multispecies ecological systems is an intriguing problem. A sufficiently complex model with the necessary predicting power requires solutions that are structurally stable. Small variations of the system parameters should not qualitatively perturb its solutions. When one is interested in just asymptotic results of evolution (as… (More)

- Mikhail I. Rabinovich, Valentin S. Afraimovich, Christian Bick, Pablo Varona
- Physics of life reviews
- 2012

Timing and dynamics of information in the brain is a hot field in modern neuroscience. The analysis of the temporal evolution of brain information is crucially important for the understanding of higher cognitive mechanisms in normal and pathological states. From the perspective of information dynamics, in this review we discuss working memory capacity,… (More)

- Mikhail I. Rabinovich, Ramón Huerta, Valentin S. Afraimovich
- Physical review letters
- 2006

We suggest a new paradigm for intelligent decision-making suitable for dynamical sequential activity of animals or artificial autonomous devices that depends on the characteristics of the internal and external world. To do it we introduce a new class of dynamical models that are described by ordinary differential equations with a finite number of… (More)

- Valentin S. Afraimovich, A Cordonet, Nikolai F. Rulkov
- Physical review. E, Statistical, nonlinear, and…
- 2002

The properties of functional relation between a noninvertible chaotic drive and a response map in the regime of generalized synchronization of chaos are studied. It is shown that despite a very fuzzy image of the relation between the current states of the maps, the functional relation becomes apparent when a sufficient interval of driving trajectory is… (More)

- Mikhail I. Rabinovich, Pablo Varona, Irma Tristan, Valentin S. Afraimovich
- Front. Comput. Neurosci.
- 2014

Recent results of imaging technologies and non-linear dynamics make possible to relate the structure and dynamics of functional brain networks to different mental tasks and to build theoretical models for the description and prediction of cognitive activity. Such models are non-linear dynamical descriptions of the interaction of the core components-brain… (More)

- Valentin S. Afraimovich, George Zaslavsky
- Chaos
- 2003

New notions of the complexity function C(epsilon;t,s) and entropy function S(epsilon;t,s) are introduced to describe systems with nonzero or zero Lyapunov exponents or systems that exhibit strong intermittent behavior with "flights," trappings, weak mixing, etc. The important part of the new notions is the first appearance of epsilon-separation of initially… (More)

- Valentin S. Afraimovich, Todd R. Young, Mehmet K. Muezzinoglu, Mikhail I. Rabinovich
- Bulletin of mathematical biology
- 2011

Emotion (i.e., spontaneous motivation and subsequent implementation of a behavior) and cognition (i.e., problem solving by information processing) are essential to how we, as humans, respond to changes in our environment. Recent studies in cognitive science suggest that emotion and cognition are subserved by different, although heavily integrated, neural… (More)