Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise

doi:10.1088/1674-1056/26/3/030502

中国物理B ›› 2017, Vol. 26 ›› Issue (3): 30502-030502.doi: 10.1088/1674-1056/26/3/030502

Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise

You-Ming Lei(雷佑铭), Hong-Xia Zhang(张红霞)

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China

收稿日期:2016-10-28 修回日期:2016-12-15 出版日期:2017-03-05 发布日期:2017-03-05
通讯作者: Hong-Xia Zhang E-mail:zhanghongxia@mail.nwpu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11672231), the Natural Science Foundation of Shaanxi Province, China (Grant No. 2016JM1010), the Fundamental Research Funds for the Central Universities, China (Grant No. 3102015ZY073), and the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University, China.

Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise

You-Ming Lei(雷佑铭), Hong-Xia Zhang(张红霞)

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China

Received:2016-10-28 Revised:2016-12-15 Online:2017-03-05 Published:2017-03-05
Contact: Hong-Xia Zhang E-mail:zhanghongxia@mail.nwpu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11672231), the Natural Science Foundation of Shaanxi Province, China (Grant No. 2016JM1010), the Fundamental Research Funds for the Central Universities, China (Grant No. 3102015ZY073), and the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University, China.

摘要/Abstract

摘要： The homoclinic and heteroclinic chaos in nonlinear systems subjected to trichotomous noise excitation are studied. The Duffing system and the Josephson-junction system are taken for example to calculate the corresponding amplitude thresholds for the onset of chaos on the basis of the stochastic Melnikov process with the mean-square criterion. It is shown that the amplitude threshold for the onset of chaos can be adjusted by changing the internal parameters of trichotomous noise, thereby inducing or suppressing chaotic behaviors in the two systems driven by trichotomous noise. The effects of trichotomous noise on the systems are verified by vanishing the mean largest Lyapunov exponent and demonstrated by phase diagrams and time histories.

关键词: trichotomous noise, chaos, Melnikov method, Lyapunov exponent

Abstract: The homoclinic and heteroclinic chaos in nonlinear systems subjected to trichotomous noise excitation are studied. The Duffing system and the Josephson-junction system are taken for example to calculate the corresponding amplitude thresholds for the onset of chaos on the basis of the stochastic Melnikov process with the mean-square criterion. It is shown that the amplitude threshold for the onset of chaos can be adjusted by changing the internal parameters of trichotomous noise, thereby inducing or suppressing chaotic behaviors in the two systems driven by trichotomous noise. The effects of trichotomous noise on the systems are verified by vanishing the mean largest Lyapunov exponent and demonstrated by phase diagrams and time histories.

Key words: trichotomous noise, chaos, Melnikov method, Lyapunov exponent

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Pq (Numerical simulations of chaotic systems) 02.50.Ey (Stochastic processes)

雷佑铭, 张红霞. Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise[J]. 中国物理B, 2017, 26(3): 30502-030502.

You-Ming Lei(雷佑铭), Hong-Xia Zhang(张红霞). Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise[J]. Chin. Phys. B, 2017, 26(3): 30502-030502.

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Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise

Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise

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