ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

Anosov dynamics

Self-oscillating system generating rough hyperbolic chaos

Topic and aim. The aim of the work is design of rough chaos generator, whose attractor implements dynamics close to Anosov flow on a manifold of negative curvature, as well as constructing and analyzing mathematical model, and
conducting circuit simulation of the dynamics using the Multisim software.

Investigated models. A mathematical model is considered that is a set of ordinary differential equations of the ninth order with algebraic nonlinearity, and a circuit representing the chaos generator is designed.

Robust chaos in autonomous time-delay system

We consider an autonomous system constructed as modification of the logistic differential equation with delay that generates successive trains of oscillations with phases evolving according to chaotic maps. The system contains two feedback loops characterized by two generally distinct  retarding time parameters. In the case of their equality, chaotic dynamics is associated with the  Smale–Williams attractor that corresponds to the double-expanding circle map for the phases of the carrier of the oscillatory trains.

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