PMID: 11909319Mar 23, 2002Paper

Targeting unknown and unstable periodic orbits

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
B Doyon, L J Dubé

Abstract

We present a method to target and subsequently control (if necessary) orbits of specified period but otherwise unknown stability and position. For complex systems where the dynamics is often mixed [e.g., coexistence of regular and chaotic regions in area-preserving (Hamiltonian) systems], this targeting algorithm offers a way to not only gently bring the system from the chaotic domain to an unstable periodic orbit (where control is applied), but also to access stable regions of phase space (where control is not necessary) from within the stochastic regions. The technique is quite general and applies equally well to dissipative or conservative discrete maps and continuous flows.

References

Jan 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·C ReylE Brun
Jan 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·E J KostelichJ A Yorke
May 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·E BarretoJ A Yorke
Mar 12, 1990·Physical Review Letters·E OttJ A Yorke
Dec 24, 1990·Physical Review Letters·W L DittoM L Spano
Dec 24, 1990·Physical Review Letters·T ShinbrotJ A Yorke
Jun 5, 2003·Chaos·Christian G. Schroer, Edward Ott

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Citations

Oct 3, 2014·Chaos·Christian BickMarc Timme
Jul 13, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Guido CiraoloPhilippe Ghendrih
Aug 25, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·C W Kulp, E R Tracy

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