Control of chaos in conservative flows

Liu Zonghua; Chen Shigang

doi:10.1103/PhysRevE.56.168

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Control of chaos in conservative flows

Liu Zonghua

Chen Shigang

CCAST (World Laboratory) P.O. Box 8730, Beijing, 100080, People’s Republic of China;
Graduate School, China Academy of Engineering Physics, P.O. Box 8009, Beijing, 100088, People’s Republic of China;
Department of Physics, Guangxi University, Nanning, 530004, People’s Republic of China

Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, People’s Republic of China

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Phys. Rev. E 56, 168 – Published 1 July, 1997

DOI: https://doi.org/10.1103/PhysRevE.56.168

Abstract

The present paper discusses the control of chaos in conservative flow. Two methods are introduced, depending on whether the perturbations to the state are variables introduced on a proportional or an additive fashion. The maximum Lyapunov exponents of new creating periods are given. The method is robust against external noise.

References (15)

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[c1] E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).

[c2] Y. Braiman and I. Goldhirsch, Phys. Rev. Lett. 66, 2545 (1991).

[c3] Y. Liu and J. R. R. Leite, Phys. Lett. A 185, 35 (1994).

[c4] E. R. Hunt, Phys. Rev. Lett. 67, 1953 (1991).

[c5] K. Pyragas, Phys. Lett. A 170, 421 (1992).

[c6] E. A. Jackson, Phys. Lett. A 151, 478 (1990).

[c7] E. A. Jackson, Physica D 50, 341 (1991).

[c8] Liu Zonghua and Chen Shigang, Phys. Rev. E 55, 199 (1997).

[c9] Liu Zonghua and Chen Shigang, Chin. Phys. Lett. 14, 85 (1997).

[c10] Y. C. Lai, M. Ding, and C. Grebogi, Phys. Rev. E 47, 86 (1993).

[c11] M. A. Matías and J. Güémez, Phys. Rev. Lett. 72, 1455 (1994).

[c12] M. A. Matías and J. Güémez, Phys. Rev. E 54, 198 (1996).

[c13] J. M. Gutiérrez, A. Iglesias, J. Güémez, and M. A. Matías, Bif. Chaos 6, 1351 (1996).

[c14] J. C. Sprott, Phys. Rev. E 50, R647 (1994).

[c15] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, New York, 1986).

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Control of chaos in conservative flows

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