Route to hyperbolic hyperchaos in a nonautonomous time-delay system

Abstract

We consider a time delay system whose excitation parameter is periodically modulated. Each new stage of excitation is seeded from the stage before the last, and due to the nonlinearity the seeding arrives with the doubled phase. As a result, the system operates as two coupled hyperbolic chaotic subsystems. Varying the relation between delay time and excitation period we affect the coupling strength between these subsystems as well as the intensity of phase doubling mechanism responsible for the hyperbolicity. Due to this the transition from non-hyperbolic to hyperbolic hyperchaos occurs. The following parts of transition scenario are revealed and analyzed: (a) intermittency as alternation of staying near a fixed point and chaotic bursts; (b) wandering between the fixed point and chaotic subset, which appears near it; (c) plain hyperchaos without hyperbolicity after termination of the visits to the fixed point; (d) transformation of hyperchaos to hyperbolic form.