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On the persistence regime for Lotka-Volterra in randomly fluctuating environments

Abstract : In this note, we study the long time behavior of Lotka-Volterra systems whose coefficients vary randomly. Benaïm and Lobry (2015) recently established that randomly switching between two environments that are both favorable to the same species may lead to different regimes: extinction of one species or the other, or persistence of both species. Our purpose here is to describe more accurately the range of parameters leading to these regimes, and the support of the invariant probability measure in case of persistence.
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https://hal.archives-ouvertes.fr/hal-01264637
Contributor : Pierre-André Zitt <>
Submitted on : Wednesday, June 14, 2017 - 11:43:04 AM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM
Document(s) archivé(s) le : Tuesday, December 12, 2017 - 3:08:01 PM

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  • HAL Id : hal-01264637, version 2
  • ARXIV : 1601.08151

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Florent Malrieu, Pierre-André Zitt. On the persistence regime for Lotka-Volterra in randomly fluctuating environments. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2017, 14, pp.733-749. ⟨hal-01264637v2⟩

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