Delayed feedback control of chaos: Bifurcation analysis

Abstract

We study the effect of time delayed feedback control in the form proposed by Pyragas on deterministic chaos in the Rössler system. We reveal the general bifurcation diagram in the parameter plane of time delay tau and feedback strength K which allows one to explain the phenomena that have been discovered in some previous works. We show that the bifurcation diagram has essentially a multileaf structure that constitutes multistability: the larger the tau, the larger the number of attractors that can coexist in the phase space. Feedback induces a large variety of regimes nonexistent in the original system, among them tori and chaotic attractors born from them. Finally, we estimate how the parameters of delayed feedback influence the periods of limit cycles in the system.