TY  - JOUR
A1  - Högele, Michael
A1  - Pavlyukevich, Ilya
T1  - Metastability in a class of hyperbolic dynamical systems perturbed by heavy-tailed Levy type noise
JF  - Stochastics and dynamic
N2  - 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.
KW  - Hyperbolic dynamical system
KW  - Morse-Smale property
KW  - physical SRB measures
KW  - stable limit cycle
KW  - small noise asymptotic
KW  - alpha-stable Levy process
KW  - multiplicative noise
KW  - Ito integral
KW  - Stratonovich integral
KW  - stochastic Marcus (canonical) differential equation
KW  - multiscale dynamics
KW  - metastability
KW  - embedded Markov chain
KW  - randomly forced Duffing equation
KW  - birhythmic behavior
Y1  - 2015
U6  - https://doi.org/10.1142/S0219493715500197
SN  - 0219-4937
SN  - 1793-6799
VL  - 15
IS  - 3
PB  - World Scientific
CY  - Singapore
ER  -