Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise  

作　　者：雷佑铭 张红霞 

机构地区：[1]Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China

出　　处：《Chinese Physics B》2017年第3期242-250,共9页中国物理B（英文版）

基　　金：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);the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University,China

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.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 

分 类 号：O415.5[理学—理论物理]