Decomposition formula and stationary measures for stochastic Lotka-Volterra system with applications to turbulent convection

Show simple item record

dc.contributor University of Helsinki, Department of Mathematics and Statistics en
dc.contributor.author Chen, Lifeng
dc.contributor.author Dong, Zhao
dc.contributor.author Jiang, Jifa
dc.contributor.author Niu, Lei
dc.contributor.author Zhai, Jianliang
dc.date.accessioned 2019-11-22T14:02:01Z
dc.date.available 2019-11-22T14:02:01Z
dc.date.issued 2019-05
dc.identifier.citation Chen , L , Dong , Z , Jiang , J , Niu , L & Zhai , J 2019 , ' Decomposition formula and stationary measures for stochastic Lotka-Volterra system with applications to turbulent convection ' , Journal de Mathematiques Pures et Appliquées , vol. 125 , pp. 43-93 . https://doi.org/10.1016/j.matpur.2019.02.013 en
dc.identifier.issn 0021-7824
dc.identifier.other PURE: 124738111
dc.identifier.other PURE UUID: 2ad025ab-b1df-48f8-8071-96c9d5661fb4
dc.identifier.other WOS: 000466257300002
dc.identifier.other ORCID: /0000-0002-3343-1726/work/66034498
dc.identifier.uri http://hdl.handle.net/10138/307239
dc.description.abstract Motivated by the remarkable works of Busse and his collaborators in the 1980s on turbulent convection in a rotating layer, we explore the long-run behavior of stochastic Lotka-Volterra (LV) systems both in pull-back trajectories and in stationary measures. A decomposition formula is established to describe the relationship between the solutions of stochastic and deterministic LV systems and the stochastic logistic equation. By virtue of this formula, it can be verified that every pull-back omega limit set is an omega limit set of the deterministic LV system multiplied by the random equilibrium of the stochastic logistic equation. The formula is also used to derive the existence of a stationary measure, its support and ergodicity. We prove the tightness of stationary measures and that their weak limits are invariant with respect to the corresponding deterministic system and supported on the Birkhoff center. The developed theory is successfully utilized to completely classify three dimensional competitive stochastic LV systems into 37 classes. The expected occupation measures weakly converge to a strongly mixing measure and all stationary measures are obtained for each class except class 27 c). Among them there are two classes possessing a continuum of random closed orbits and strongly mixing measures supported on the cone surfaces, which weakly converge to the Haar measures of periodic orbits as the noise intensity vanishes. The class 27 c) is an exception, almost every pull-back trajectory cyclically oscillates around the boundary of the stochastic carrying simplex characterized by three unstable stationary solutions. The limit of the expected occupation measures is neither unique nor ergodic. These are consistent with symptoms of turbulence. (C) 2019 Elsevier Masson SAS. All rights reserved. en
dc.format.extent 51
dc.language.iso eng
dc.relation.ispartof Journal de Mathematiques Pures et Appliquées
dc.rights en
dc.subject Stochastic Lotka-Volterra system en
dc.subject Stationary measure en
dc.subject Ergodicity en
dc.subject Support en
dc.subject Stochastically cyclical oscillation en
dc.subject Turbulence en
dc.subject ELLIPTIC-EQUATIONS en
dc.subject 111 Mathematics en
dc.title Decomposition formula and stationary measures for stochastic Lotka-Volterra system with applications to turbulent convection en
dc.type Article
dc.description.version Peer reviewed
dc.identifier.doi https://doi.org/10.1016/j.matpur.2019.02.013
dc.type.uri info:eu-repo/semantics/other
dc.type.uri info:eu-repo/semantics/acceptedVersion
dc.contributor.pbl

Files in this item

Total number of downloads: Loading...

Files Size Format View
main.pdf 741.5Kb PDF View/Open

This item appears in the following Collection(s)

Show simple item record