Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation

doi:10.1088/1674-1056/19/9/090306

Abstract This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincaré map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using non-feedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to period-motions by adding an excitation term.

Keywords: relative rotation nonlinear dynamical system parametric excitation chaotic control

Received: 16 November 2009
Revised: 11 December 2009
Accepted manuscript online:

PACS:	0340D
	0313

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60704037), the Natural Science Foundation of Hebei Province, China (Grant No. F2010001317) and the Doctor Foundation of Yanshan University of China (Grant No. B451).

Cite this article:

Shi Pei-Ming(时培明), Han Dong-Ying(韩东颖), and Liu Bin(刘彬) Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation 2010 Chin. Phys. B 19 090306

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Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation

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