Levy noise-driven escape from arctangent potential wells
- The escape from a potential well is an archetypal problem in the study of stochastic dynamical systems, representing real-world situations from chemical reactions to leaving an established home range in movement ecology. Concurrently, Levy noise is a well-established approach to model systems characterized by statistical outliers and diverging higher order moments, ranging from gene expression control to the movement patterns of animals and humans. Here, we study the problem of Levy noise-driven escape from an almost rectangular, arctangent potential well restricted by two absorbing boundaries, mostly under the action of the Cauchy noise. We unveil analogies of the observed transient dynamics to the general properties of stationary states of Levy processes in single-well potentials. The first-escape dynamics is shown to exhibit exponential tails. We examine the dependence of the escape on the shape parameters, steepness, and height of the arctangent potential. Finally, we explore in detail the behavior of the probability densities ofThe escape from a potential well is an archetypal problem in the study of stochastic dynamical systems, representing real-world situations from chemical reactions to leaving an established home range in movement ecology. Concurrently, Levy noise is a well-established approach to model systems characterized by statistical outliers and diverging higher order moments, ranging from gene expression control to the movement patterns of animals and humans. Here, we study the problem of Levy noise-driven escape from an almost rectangular, arctangent potential well restricted by two absorbing boundaries, mostly under the action of the Cauchy noise. We unveil analogies of the observed transient dynamics to the general properties of stationary states of Levy processes in single-well potentials. The first-escape dynamics is shown to exhibit exponential tails. We examine the dependence of the escape on the shape parameters, steepness, and height of the arctangent potential. Finally, we explore in detail the behavior of the probability densities of the first-escape time and the last-hitting point.…
Author details: | Karol CapałaORCiD, Amin PadashORCiD, Aleksei ChechkinORCiDGND, Babak ShokriORCiD, Ralf MetzlerORCiDGND, Bartłomiej DybiecORCiD |
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DOI: | https://doi.org/10.1063/5.0021795 |
ISSN: | 1054-1500 |
ISSN: | 1089-7682 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/33380056 |
Title of parent work (English): | Chaos : an interdisciplinary journal of nonlinear science |
Publisher: | American Institute of Physics |
Place of publishing: | Woodbury, NY |
Publication type: | Article |
Language: | English |
Date of first publication: | 2020/12/01 |
Publication year: | 2020 |
Release date: | 2023/10/10 |
Volume: | 30 |
Issue: | 12 |
Article number: | 123103 |
Number of pages: | 15 |
Funding institution: | Faculty of Physics, Astronomy and Applied Computer Science under the DSC; scheme [2019-N17/MNS/000013]; PLGrid Infrastructure; German Science; Foundation (DFG)German Research Foundation (DFG) [ME 1535/7-1]; Foundation for Polish Science (Fundacja na rzecz Nauki Polskiej, FNP) |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik | |
Peer review: | Referiert |