Probability density and stochastic stability for the coupled Van der Pol oscillator system. Issue 1 (1st January 2018)

• Record Type: Journal Article
• Authors: Li, Shenghong; Zhu, Quanxin
• Editors: Lu, Zudi
• Is Part Of: Cogent mathematics & statistics. Volume 5:Issue 1(2018)
• Publication Date: 2018-01-01
• Subjects: stochastic averaging method -- FPK equation -- almost sure asymptotic stability -- maximal Lyapunov exponent; Mathematics -- Periodicals; Statistics -- Periodicals; Mathematics; Statistics; Periodicals; 510
• DOI: 10.1080/23311835.2018.1431092
• Languages: English
• ISSNs: 2574-2558

Abstract

Abstract: In this paper, the probability density and almost sure asymptotic stability of the coupled Van der Pol oscillator system under the noise excitations are investigated. Through the stochastic averaging method and slow changing process theorem, averaged Fokker–Planck–Kolmogorov equation and exact solution of the dynamical system are obtained. Especially, the marginal density functions of the system excited by the additive white noises are derived. Then, the effects of coupled parameters and noise parameters on the marginal density functions are discussed through the numerical figures. In addition, the almost sure asymptotic stability under the parametric excitation by means of the maximal Lyapunov exponent is studied, and the stable demarcation points about noise intensity are presented.