Delayed feedback control of periodic orbits in autonomous systems

Details Delayed feedback control of periodic orbits in autonomous systems Delayed feedback control of periodic orbits in autonomous systems

1998-08-06

arxiv.org/abs/chao-dyn/9808007v1

Phys. Rev. Lett. 81 (1998) 562

Nonlinear Sciences

Chaotic Dynamics

4 pages, Revtex, manuscript also available at ftp://athene.fkp.physik.th-darmstadt.de/pub/publications/wolfram/prl_98a/ or a

Scientific paper

10.1103/PhysRevLett.81.562

For controlling periodic orbits with delayed feedback methods the periodicity has to be known a priori. We propose a simple scheme, how to detect the period of orbits from properties of the control signal, at least if a periodic but nonvanishing signal is observed. We analytically derive a simple expression relating the delay, the control amplitude, and the unknown period. Thus, the latter can be computed from experimentally accessible quantities. Our findings are confirmed by numerical simulations and electronic circuit experiments

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