Lotka-Volterra with randomly fluctuating environments: a full description

Abstract : In this note, we study the long time behavior of Lotka-Volterra systems whose coefficients vary randomly. Bena¨m and Lobry established that randomly switching between two environments that are both favorable to the same species may lead to four different regimes: almost sure extinction of one of the two species, random extinction of one species or the other and persistence of both species. Our purpose here is to provide a complete description of the model. In particular, we show that any couple of environments may lead to the four different behaviours of the stochastic process depending on the jump rates.
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https://hal.archives-ouvertes.fr/hal-01345626
Contributor : Florent Malrieu <>
Submitted on : Thursday, July 14, 2016 - 6:15:37 PM
Last modification on : Thursday, January 17, 2019 - 3:02:02 PM

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  • HAL Id : hal-01345626, version 1
  • ARXIV : 1607.04395

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Florent Malrieu, Tran Hoa Phu. Lotka-Volterra with randomly fluctuating environments: a full description. 2016. ⟨hal-01345626⟩

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