TY  - JOUR
A1  - Pavlyukevich, Ilya
A1  - Li, Yongge
A1  - Xu, Yong
A1  - Chechkin, Aleksei V.
T1  - Directed transport induced by spatially modulated Levy flights
JF  - Journal of physics : A, Mathematical and theoretical
N2  - In this paper we study the dynamics of a particle in a ratchet potential subject to multiplicative alpha-stable Levy noise, alpha is an element of(0, 2), in the limit of a noise amplitude epsilon -> 0. We compare the dynamics for Ito and Marcus multiplicative noises and obtain the explicit asymptotics of the escape time in the wells and transition probabilities between the wells. A detailed analysis of the noise-induced current is performed for the Seebeck ratchet with a weak multiplicative noise for alpha is an element of(0, 2].
KW  - Levy flights
KW  - multiplicative noise
KW  - Seebeck ratchet
KW  - directed transport
Y1  - 2015
U6  - https://doi.org/10.1088/1751-8113/48/49/495004
SN  - 1751-8113
SN  - 1751-8121
VL  - 48
IS  - 49
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
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  - 
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  -