The instability probability density evolution of the bistable system driven by Gaussian colored noise and white noise

Yong-Feng Guo, Fang Wei, Bei Xi and Jian-Guo Tan

Physica A: Statistical Mechanics and its Applications, 2018, vol. 503, issue C, 200-208

Abstract: In this paper, we studied the instability probability density evolution of the bistable system driven by Gaussian colored noise and white noise. Firstly, the bistable system is linearized in the initial area by applying Ω expansion theory of the Green function. Next, the time-dependent non-stationary state solutionpx,t of the Fokker–Planck equation for the linearized system is obtained by using eigenvalue and eigenvector theory. Finally, the effect of the time t, the colored noise intensity α, the correlation time τ and the white noise intensity D on p(x,t) are analyzed. Numerical computation results show that: p(x,t) is a monotonic decreasing function of variable x and intensity α. In contrast,p(x,t) is a monotonic increasing function of correlation time τ. Moreover, p(x,t) appears a peak with the increasing of t when x or D are fixed values respectively.

Keywords: Bistable system; Gaussian noise; Eigenvalue and eigenvector theory; Non-stationary state solution (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:503:y:2018:i:c:p:200-208

DOI: 10.1016/j.physa.2018.02.208

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