TY  - INPR
A1  - Högele, Michael
A1  - Pavlyukevich, Ilya
T1  - Metastability of Morse-Smale dynamical systems perturbed by heavy-tailed Lévy type noise
N2  - We consider a general class of finite dimensional deterministic dynamical systems with finitely many local attractors each of which supports a unique ergodic probability measure, which includes in particular the class of Morse–Smale systems in any finite dimension. The dynamical system is perturbed by a multiplicative non-Gaussian heavytailed Lévy type noise of small intensity ε > 0. Specifically we consider perturbations leading to a Itô, Stratonovich and canonical (Marcus) stochastic differential equation. The respective asymptotic first exit time and location problem from each of the domains of attractions in case of inward pointing vector fields in the limit of ε-> 0 has been investigated by the authors. We extend these results to domains with characteristic boundaries and show that the perturbed system exhibits a metastable behavior in the sense that there exits a unique ε-dependent time scale on which the random system converges to a continuous time Markov chain switching between the invariant measures. As examples we consider α-stable perturbations of the Duffing equation and a chemical system exhibiting a birhythmic behavior.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 5 
KW  - hyperbolic dynamical system
KW  - Morse-Smale property
KW  - stable limit cycle
KW  - small noise asymptotic
KW  - multiplicative noise
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70639
SN  - 2193-6943
VL  - 3
IS  - 5
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  -