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Affiliation of Author(s):航空学院

Title of Paper:Noise-Induced Chaos in a Piecewise Linear System

Journal:INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

Key Words:Piecewise linear system intermittent switching behavior noise-induced chaos MFPT

Abstract:In the present paper, the phenomenon of noise-induced chaos in a piecewise linear system that is excited by Gaussian white noise is investigated. Firstly, the global dynamical behaviors of the deterministic piecewise linear system are investigated numerically in advance by using the generalized cell-mapping digraph (GCMD) method. Then, based on these global properties, the system that is excited by Gaussian white noise is introduced. Then, it is simplified by the stochastic averaging method, through which, a four-dimensional averaged Ito system is finally obtained. In order to reveal the phenomenon of noise-induced chaos quantitatively, MFPT (the mean first-passage time) is selected as the measure. The expression for MFPT is formulated by using the singular perturbation method and then a rather simple representation is obtained via the Laplace approximation, and within which, the concept of quasi-potential is introduced. Furthermore, with the rays method, the MFPT under a certain set of parameters is estimated. However, within the process of analysis, the authors had to face a difficult problem concerning the ill-conditioned matrix, which is the obstacle for the estimation of MFPT, which was then solved by applying one more approximation. Finally, the result is compared with the numerical one that is obtained by the Monte Carlo simulation.

ISSN No.:0218-1274

Translation or Not:no

Date of Publication:2017-08-01

Co-author:Kong, Chen

Correspondence Author:lxb