Effects of white noise in multistable dynamics | Zendy

Xinfu Chen | Zendy; Carey Caginalp | Zendy; Jianghao Hao | Zendy; Yajing Zhang | Zendy

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Effects of white noise in multistable dynamics

Author(s) -

Xinfu Chen,

Carey Caginalp,

Jianghao Hao,

Yajing Zhang

Publication year - 2013

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2013.18.1805

Subject(s) - white noise , invariant measure , invariant (physics) , measure (data warehouse) , statistical physics , limit (mathematics) , noise (video) , mathematics , dynamics (music) , physics , mathematical analysis , mathematical physics , computer science , statistics , ergodic theory , acoustics , artificial intelligence , image (mathematics) , database

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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