Динамические системы

Aim. The aim of the paper is investigation of the development of the fixed-point method and mapping degree theory associated with the names of P. Bohl, L. Brouwer, K. Borsuk, S. Ulam and others and its application to study of the trajectories of dynamical systems behavior and stable states of ordered media.

Topic. A review of the basic dynamical models of neural activity is presented and individual features of their behavior are discussed, which can be used as a basis for the subsequent development and construction of various configurations of neural networks. The work contains both new original results and generalization of already known ones published earlier in different journals.

A mathematical model with 2.5 degrees of freedom under external periodic stimulation is investigated. It is a model of chaotic oscillator with bipolar transistor as an active element. It is shown that external periodic stimulation of the oscillator of such system allows to generate chaotic pulse stream.

DOI: 10.18500/0869-6632-2015-23-2-37-46

The paper is a review of well-known in nonlinear dynamics models with low dimensional of phase space and quasiperiodic behavior. Also new results related to analysis of many-frequencies quasiperiodic oscillations for models with external action and coupled oscillators are discussed.

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In the present work the new approach to numerical research of the concrete multi­dimensional and multiparametric dynamic systems is submitted. The offered approach, in part realized and approved, is based on computer calculation of phase trajectories and on use of pattern recognition methods.