Multi-dimensional chaos initiated by short pulses in non-autonomous radio-physical generator

Abstract

A non-autonomous model of the Anishchenko–Astakhov generator in the regime of periodic and chaotic self-oscillations is considered. A periodic sequence of short pulses is considered as an external force. It is shown that the synchronization picture is close in structure to the classical synchronization picture observed in a two-dimensional system, but the pulse action leads to the excitation of chaotic oscillations, including those characterized by a different spectrum of Lyapunov exponents. In particular, it is shown appearance of hyperchaos and chaos with additional close to zero Lyapunov exponent. Phenomenological scenarios for the development of multi-dimensional chaos related to destruction of two-frequency tori are described. Hyperchaos is formed via hierarchy of discrete Shilnikov attractors arise as a result of sequence of Neimark-Sacker bifurcations. Chaos with additional close to zero Lyapunov exponent occurs as impact of saddle tori appeared via sequence of torus-doubling bifurcations.