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 correspond...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.展开更多
The stochastic multiresonance behavior for a fractional linear oscillator with random system frequency is investigated. The fluctuation of the system frequency is a quadratic trichotomous noise, the memory kernel of t...The stochastic multiresonance behavior for a fractional linear oscillator with random system frequency is investigated. The fluctuation of the system frequency is a quadratic trichotomous noise, the memory kernel of the fractional oscillator is modeled as a Mittag–Leffler function. Based on linear system theory, applying Laplace transform and the definition of fractional derivative, the expression of the system output amplitude(SPA) is obtained. Stochastic multiresonance phenomenon is found on the curves of SPA versus the memory time and the memory exponent of the fractional oscillator, as well as versus the trichotomous noise amplitude. The SPA depends non-monotonically on the stationary probability of the trichotomous noise, on the viscous damping coefficient and system characteristic frequency of the oscillator, as well as on the driving frequency of external force.展开更多
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)+1 种基金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
文摘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.
基金Supported by National Natural Science Foundation of China under Grant No.61134002
文摘The stochastic multiresonance behavior for a fractional linear oscillator with random system frequency is investigated. The fluctuation of the system frequency is a quadratic trichotomous noise, the memory kernel of the fractional oscillator is modeled as a Mittag–Leffler function. Based on linear system theory, applying Laplace transform and the definition of fractional derivative, the expression of the system output amplitude(SPA) is obtained. Stochastic multiresonance phenomenon is found on the curves of SPA versus the memory time and the memory exponent of the fractional oscillator, as well as versus the trichotomous noise amplitude. The SPA depends non-monotonically on the stationary probability of the trichotomous noise, on the viscous damping coefficient and system characteristic frequency of the oscillator, as well as on the driving frequency of external force.
