Ott, Edward; Grebogi, Celso; Yorke, James A. Controlling chaos. (English) Zbl 0964.37501 Phys. Rev. Lett. 64, No. 11, 1196-1199 (1990); Erratum, No. 23, 2837 (1990). Summary: The authors show that one can convert a chaotic attractor to any one of a large number of possible attracting time-periodic motions by making only small time-dependent perturbations of an available system parameter. The method utilizes delay coordinate embedding, and so is applicable to experimental situations in which apriori analytical knowledge of the system dynamics is not available. Important issues include the length of the chaotic transience preceding the periodic motion, and the effect of noise. A numerical example is given. Cited in 13 ReviewsCited in 1262 Documents MSC: 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 34C25 Periodic solutions to ordinary differential equations 37C70 Attractors and repellers of smooth dynamical systems and their topological structure Keywords:chaotic attractor PDF BibTeX XML Cite \textit{E. Ott} et al., Phys. Rev. Lett. 64, No. 11, 1196--1199 (1990; Zbl 0964.37501) Full Text: DOI OpenURL References: [1] C. Grebogi, Phys. Rev. A 37 pp 1711– (1988) [2] C. Grebogi, Phys. Rev. A 36 pp 3522– (1987) [3] D. Auerbach, Phys. Rev. Lett. 58 pp 2387– (1987) [4] H. Hata, Prog. Theor. Phys. 78 pp 511– (1987) [5] A. Katok, Publ. Math. IHES 51 pp 137– (1980) [6] R. Bowen, Trans. Am. Math. Soc. 154 pp 377– (1971) [7] E. Ott, in: Chaos: Proceedings of a Soviet-American Conference (1990) [8] F. Takens, in: Dynamical Systems and Turbulence (1981) [9] N. H. Packard, Phys. Rev. Lett. 45 pp 712– (1980) [10] G. H. Gunaratne, Phys. Rev. Lett. 63 pp 1– (1989) [11] C. Grebogi, Phys. Rev. Lett. 57 pp 1284– (1986) [12] P. Romeiras, Phys. Rev. A 36 pp 5365– (1987) [13] A. Hubler, Helv. Phys. Acta 62 pp 343– (1989) [14] T. B. Fowler, IEEE Trans. Autom. Control 34 pp 201– (1989) · Zbl 0677.93072 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.