| Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation |
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| 作者姓名： | 时培明 韩东颖 刘彬 |
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| 作者单位： | Key Laboratory of Measurement Technology and Instrument of Hebei Province Yanshan University, Qinhuangdao 066004, China; College of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China;College of Vehicles and Energy Yanshan University, Qinhuangdao 066004, China;College of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China |
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| 基金项目： | 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). |
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| 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, Poincar 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.
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| 关 键 词： | relative rotation nonlinear dynamical system parametric excitation chaotic control |
| 收稿时间： | 2009-11-16 |
Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation |
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| Shi Pei-Ming,Han Dong-Ying and Liu Bin.Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation[J].Chinese Physics B,2010,19(9):90306-090306. |
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| Authors: | Shi Pei-Ming Han Dong-Ying and Liu Bin |
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| Affiliation: | College of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China; College of Vehicles and Energy Yanshan University, Qinhuangdao 066004, China; Key Laboratory of Measurement Technology and Instrument of Hebei Province Yanshan University, Qinhuangdao 066004, China; College of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China |
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| 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. |
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| Keywords: | relative rotation nonlinear dynamical system parametric excitation chaotic control |
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