fbaroni's Afraimovich [4 articles]

Abstract

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 time goes to infinity), then the problem has a straightforward mathematical image involving simple attractors (fixed points or limit cycles) of a dynamical system. However, for an accurate prediction of evolution, the ...

Abstract

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 fixed points). These are not suitable for the description of reproducible transient sequential neural dynamics. In this paper we present the concept of a stable heteroclinic sequence (SHS), which is not an attractor. ...

Abstract

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 activity of large-scale brain networks in the presence of noise. Such transients may consist of a sequential switching between different metastable cognitive states. ...

Abstract

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 possibilities at the decision points, and also include rules solving this uncertainty. Our approach is based on the competition between possible cognitive states using their stable transient dynamics. ...