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Delayed feedback control of chaos: Bifurcation analysis
preprintposted on 2005-07-19, 14:45 authored by Alexander BalanovAlexander Balanov, Natalia JansonNatalia Janson, E. Scholl
We study the effect of time delayed feedback control in the form proposed by Pyragas on deterministic chaos in the Rossler system. We reveal the general bifurcation diagram in the parameter plane of time delay 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 multi-leaf structure that constitutes multistability: the larger the time delay , the larger the number of attractors that can coexist in the phase space. Feedback induces a large variety of regimes non-existent 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.
- Mathematical Sciences
NotesThis pre-print has been submitted, and accepted, to the journal, Physical review E [© American Institute of Physics]. The definitive version, BALANOV, A.G., JANSON, N.B and SCHOLL, E., 2005. Delayed feedback control of chaos: Bifurcation analysis. Physical review E, 71(1): art. no. 016222, is available at http://pre.aps.org/.