Systems of Four Alternately Excited Non-autonomous Oscillators

Abstract

This chapter is devoted to non-autonomous models generating successive trains of oscillations with phase chaotically varying from one train to the other. In contrast to Chap. 4, here we examine dynamics in the phase space of larger dimensions; so, the models arc composed of four oscillators activating by turns (usually in pairs). Particularly, we consider a model, in which evolution of the phases in successive epochs of activity is described by the Arnold cat map and by a hyperchaotic torus map that has two positive Lyapunov exponents. Then, a system will be discussed that can be thought of as being composed of two coupled pairs of oscillators, each of which corresponds to a system with hyperbolic attractor of Smale-Williams type in the Poincare map. This may be regarded as initial step of a research program for ensembles of coupled elements with hyperbolic chaotic dynamics, like coupled map lattices considered, e.g. in (Bunimovich and Sinai, 1988; 1993; Bricmont and Kupiainen, 1997; Jarvenpaa, 2005), but on a base of concrete physically realizable systems.