dynamical systems

Purpose of this work is to construct a model of infection spread in the form of a lattice of probabilistic cellular automata, which takes into account the inertial nature of infection transmission between individuals. Identification of the relationship between the spatial and temporal dynamics of the model depending on the probability of migration of individuals.

Methods. The numerical simulation of stochastic dynamics of the lattice of cellular automata by the Monte Carlo method.

Purpose of this work is to build a model of the infection spread in the form of a system of differential equations that takes into account the inertial nature of the transfer of infection between individuals. Methods. The paper presents a theoretical and numerical study of the structure of the phase space of the system of ordinary differential equations of the mean field model. Results. A modified SIRS model of epidemic spread is constructed in the form of a system of ordinary differential equations of the third order.

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. 

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.  

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.

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. Method. The study is based on an analysis of the fundamental works of the mentioned mathematicians 1900–1930’s, as well as later results of N. Levinson, G. Volovik, V. Mineev, J. Toland and H. Hofer of an applied nature. Results.