Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise

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

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.

Keywords: trichotomous noise chaos Melnikov method Lyapunov exponent

Received: 28 October 2016
Revised: 15 December 2016
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	05.45.Pq	(Numerical simulations of chaotic systems)
	02.50.Ey	(Stochastic processes)

Fund: 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.

Corresponding Authors: Hong-Xia Zhang
E-mail: zhanghongxia@mail.nwpu.edu.cn

Cite this article:

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

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Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise

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