Olga B. Isaeva

Hyperbolic Chaos and Other Phenomena of Complex Dynamics Depending on Parameters in a Nonautonomous System of Two Alternately Activated Oscillators

We provide a multiparameter analysis of dynamics in a nonautonomous system of two alternately exciting self-oscillatory elements that are able to demonstrate a uniformly chaotic attractor of Smale–Williams type in the stroboscopic Poincare map. Parameter space charts of regular and chaotic regimes are presented. Possible scenarios of the onset of hyperbolic chaos are discussed. The numerical studies are supplemented by experimental results obtained for a laboratory electronic device.

Complex Analytic Dynamics Phenomena in a System of Coupled Nonautonomous Oscillators with Alternative Excitation

A model system of two coupled nonautonomous oscillators is proposed, in which the phenomena of complex analytic dynamics (Mandelbrot and Julia sets, etc.) characteristic of complex logistic maps are realized. The idea underlying the model is based on the mechanism of alternative excitation transfer from one subsystem to another and on the method (well known in the theory of oscillations) of slowly varying complex amplitudes.