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	Identification of unstable fixed points for randomly perturbed dynamical systems with multistability
	Chen, Xian ; Jia, Chen
	2017
关键词	Bistability Diffusion process Downhill timescale Maximum inequality COMPLEX DISEASES DIFFUSION ESCAPE
英文摘要	Multistability, especially bistability, is one of the most important nonlinear phenomena in deterministic and stochastic dynamics. The identification of unstable fixed points for randomly perturbed dynamical systems with multistability has drawn increasing attention in recent years. In this paper, we provide a rigorous mathematical theory of the previously proposed data-driven method to identify the unstable fixed points of multistable systems. Specifically, we define a family of statistics which can be estimated by practical time-series data and prove that the local maxima of this family of statistics will converge to the unstable fixed points asymptotically. During the proof of the above result, we obtain two mathematical by-products which are interesting in their own right. We prove that the downhill timescale for randomly perturbed dynamical systems is log(1/epsilon), different from the uphill timescale of e(v/epsilon) for some V > 0 predicted by the Freidlin-Wentzell theory. Moreover, we also obtain an L-P maximum inequality for randomly perturbed dynamical systems and a class of diffusion processes. (C) 2016 Elsevier Inc. All rights reserved.; China Postdoctoral Science Foundation [2015M570007]; SCI(E); ARTICLE; 1; 521-545; 446
语种	英语
出处	SCI
出版者	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/475558]
专题	数学科学学院
推荐引用方式 GB/T 7714	Chen, Xian,Jia, Chen. Identification of unstable fixed points for randomly perturbed dynamical systems with multistability. 2017-01-01.

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