Metastability in a class of hyperbolic dynamical systems perturbed by heavy-tailed Levy type noise
- We consider a finite dimensional deterministic dynamical system with finitely many local attractors K-iota, each of which supports a unique ergodic probability measure P-iota, perturbed by a multiplicative non-Gaussian heavy-tailed Levy noise of small intensity epsilon > 0. We show that the random system exhibits a metastable behavior: there exists a unique epsilon-dependent time scale on which the system reminds of a continuous time Markov chain on the set of the invariant measures P-iota. In particular our approach covers the case of dynamical systems of Morse-Smale type, whose attractors consist of points and limit cycles, perturbed by multiplicative alpha-stable Levy noise in the Ito, Stratonovich and Marcus sense. As examples we consider alpha-stable Levy perturbations of the Duffing equation and Pareto perturbations of a biochemical birhythmic system with two nested limit cycles.
Author details: | Michael HögeleGND, Ilya Pavlyukevich |
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DOI: | https://doi.org/10.1142/S0219493715500197 |
ISSN: | 0219-4937 |
ISSN: | 1793-6799 |
Title of parent work (English): | Stochastics and dynamic |
Publisher: | World Scientific |
Place of publishing: | Singapore |
Publication type: | Article |
Language: | English |
Year of first publication: | 2015 |
Publication year: | 2015 |
Release date: | 2017/03/27 |
Tag: | Hyperbolic dynamical system; Ito integral; Morse-Smale property; Stratonovich integral; alpha-stable Levy process; birhythmic behavior; embedded Markov chain; metastability; multiplicative noise; multiscale dynamics; physical SRB measures; randomly forced Duffing equation; small noise asymptotic; stable limit cycle; stochastic Marcus (canonical) differential equation |
Volume: | 15 |
Issue: | 3 |
Number of pages: | 26 |
Funding institution: | Berlin Mathematical School (BMS); University of Potsdam; University of Jena; IRTG 1740 Dynamical Phenomena in Complex Networks: Fundamentals and Applications |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |