hyperbolic attractor

Examples of model non­autonomous systems are constructed and studied possessing hyperbolic attractors of Smale–Williams type in their stroboscopic maps. The dynamics is determined by application of a periodic sequence of kicks, in such way that on one period of the external driving the angular coordinate, or the phase of oscillations, behaves in accordance with an expanding circle map with chaotic dynamics.

Chaotic dynamics of a system of four nonlinear coupled non-identical Landau-Stuart oscillators is considered. Subsystems are activated alternately by pairs due to aslow variation of their parameters responsible for the Andronov–Hopf bifurcation. It is shown, that system dynamics depends of coupling type. Different types of phase map (Bernoulli type map) are obtained in Poincar´ e section depending of coupling. Some systems with different type of coupling corresponded to «maximum» and «minimum» chaos are investigated.