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.


We show that in an inhomogeneous self-sustained oscillatory me dium the destruction of perfect clusters of partial synchronization, that is induced both by varying the control parameter and by noise, leads to the onset of chaotic behavior. We study the mechanisms of chaos formation in both cases. It is demonstrated that as parameters change, the transition to chaos in the deterministic medium can result from a hard (subcritical) period-doubling bifurcation and can be ac companied by intermittency.

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.

Dynamics of the Coupled Nonautonomous Nonlinear Oscillators with Irrational Driving Frequencies Ratio

In present article the system of the two coupled nonautonomous nonlinear oscillators with irrational driving frequencies ratio is investigated experimentally. The existence regions of the various dynamical types are presented on the external excitation parameter plan. It is shown that in the case of irrational driving frequencies ratio and as result invariance system dynamics due to phases or phase difference of excitation in phase space exist torus, double torus, strange nonchaotic attractor, chaos and hyperchaos only.

Influence of the Co-Phase Harmonis Excitation on the Dynamics of the Two Coupled Period Doubling Systems

The system of two coupled maps under in-phase harmonic forcing is investigated numerically. By calculating of the lyapunov exponent spectrum the structure of control parameters space is investigated, the existence regions of the various multistable states are presented, the structure of the basins of attraction is studed.

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.