Effects of white noise in multistable dynamics

Xinfu Chen; Carey Caginalp; Jianghao Hao; Yajing Zhang

doi:10.3934/dcdsb.2013.18.1805

Article Contents

2013, Volume 18, Issue 7: 1805-1825. Doi: 10.3934/dcdsb.2013.18.1805

This issue Previous Article Attractivity for neutral functional differential equations Next Article Phase-locked trajectories for dynamical systems on graphs

Effects of white noise in multistable dynamics

1.
School of Mathematical Sciences, Shanxi University, Taiyuan, 030006
2.
Division of Applied Mathematics, Brown University, Providence, RI 02912
3.
School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006

Received: December 31, 2012

Revised: March 31, 2013

Published: August 2013

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Abstract

We study the invariant measure of multistable dynamics under the influence of white noise. We show that the invariant measure exists and in the limit of vanishing white noise, the invariant measure approaches a Dirac type measure concentrated at the most stable equilibria if fluctuations are uniform; however, a lesser stable equilibrium may be selected by the fluctuation if its ability to fluctuate is sufficiently smaller than other stable equilibria. Certain related mathematical issues are also addressed.

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Mathematics Subject Classification: Primary: 37H10, 60H40; Secondary: 35Q84.

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