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

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

中国物理B ›› 2010, Vol. 19 ›› Issue (9): 90306-090306.doi: 10.1088/1674-1056/19/9/090306

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

刘彬¹, 韩东颖², 时培明³

(1)College of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China; (2)College of Vehicles and Energy Yanshan University, Qinhuangdao 066004, China; (3)Key Laboratory of Measurement Technology and Instrument of Hebei Province Yanshan University, Qinhuangdao 066004, China; College of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China

收稿日期:2009-11-16 修回日期:2009-12-11 出版日期:2010-09-15 发布日期:2010-09-15
基金资助:
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).

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

Shi Pei-Ming(时培明)^a)b)†, Han Dong-Ying(韩东颖)^c), and Liu Bin(刘彬)^b)

^a Key Laboratory of Measurement Technology and Instrument of Hebei Province Yanshan University, Qinhuangdao 066004, China; ^b College of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China; ^c College of Vehicles and Energy Yanshan University, Qinhuangdao 066004, China

Received:2009-11-16 Revised:2009-12-11 Online:2010-09-15 Published:2010-09-15
Supported by:
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).

摘要/Abstract

摘要： 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.

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.

Key words: relative rotation, nonlinear dynamical system, parametric excitation, chaotic control

中图分类号:

0340D

时培明, 韩东颖, 刘彬. Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation[J]. 中国物理B, 2010, 19(9): 90306-090306.

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[J]. Chin. Phys. B, 2010, 19(9): 90306-090306.

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

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

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