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.


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
Full Text: DOI


[1] C. Grebogi, Phys. Rev. A 37 pp 1711– (1988) · doi:10.1103/PhysRevA.37.1711
[2] C. Grebogi, Phys. Rev. A 36 pp 3522– (1987) · doi:10.1103/PhysRevA.36.3522
[3] D. Auerbach, Phys. Rev. Lett. 58 pp 2387– (1987) · doi:10.1103/PhysRevLett.58.2387
[4] H. Hata, Prog. Theor. Phys. 78 pp 511– (1987) · doi:10.1143/PTP.78.511
[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) · doi:10.1103/PhysRevLett.45.712
[10] G. H. Gunaratne, Phys. Rev. Lett. 63 pp 1– (1989) · doi:10.1103/PhysRevLett.63.1
[11] C. Grebogi, Phys. Rev. Lett. 57 pp 1284– (1986) · doi:10.1103/PhysRevLett.57.1284
[12] P. Romeiras, Phys. Rev. A 36 pp 5365– (1987) · doi:10.1103/PhysRevA.36.5365
[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 · doi:10.1109/9.21099
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.