Izvestiya of Saratov University.
ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)


показатель Ляпунова

On the effect of noise on quasiperiodicity of different dimensions, including the quasiperiodic Hopf bifurcation

Background and Objectives: The basic model of study is the simplest three - dimensional map with two-frequency and three-frequency quasiperiodicity at adding of noise. The main objective is to examine the effect of noise on the quasiperiodic Hopf bifurcation of the 3-torus birth. Materials and Methods: To study the torus map in the presence of noise we use such numerical methods as computing of Lyapunov exponents, calculation of Fourier spectra, drawing of attractor portraits.

О влиянии шума на квазипериодичность разной размерности, включая квазипериодическую бифуркацию Хопфа

Работа посвящена численному исследованию воздействия аддитивного шума на дискретную систему, в которой реализуются квазипериодические режимы разной размерности. Дан обзор основных особенностей, наблюдающихся в системе с двухчастотной квазипериодичностью (отображение окружности) в присутствии шума.

Chaos in the System of Three Coupled Rotators: from Anosov Dynamics to Hyperbolic Attractor

The work presents an example of a system with chaotic dynamics built of three rotators by modifying a conservative system with hyperbolic Anosov dynamics. Results of a computational study of chaotic dynamics are considered (portraits of attractors, time dependences of the variables, Lyapunov exponents, and spectra) and good correspondence is observed between the dynamics on the attractor of the proposed system with the reduced model, characterized by the Anosov dynamics at appropriately defined energy.

From Anosov’s Dynamics on a Surface of Negative Curvature to Electronic Generator of Robust Chaos

Background and Objectives: Systems with hyperbolic chaos should be of preferable interest due to structural stability (roughness) that implies insensitivity to variation of parameters, manufacturing imperfections, interferences, etc. However, until recently, exclusively formal mathematical examples of this kind of dynamical behavior were known. It makes sense to turn to purposeful constructing the systems with hyperbolic dynamics appealing to tools of physics and electronics.

Lorenz Attractor in a System with Delay: an Example of Pseudogyperbolic Chaos

Background and Objectives: The work contributes to a research direction aimed at search for and construction of physically realizable systems, which could fill the mathematical theory of pseudo-hyperbolic dynamics with physical content. Chaotic attractors belonging to this class generate genuine chaos that does not degrade under small variations of parameters and functions in dynamical equations.