# Lotka–Volterra with randomly fluctuating environments or “how switching between beneficial environments can make survival harder”

@article{Benaim2016LotkaVolterraWR, title={Lotka–Volterra with randomly fluctuating environments or “how switching between beneficial environments can make survival harder”}, author={M. Benaim and Claude Lobry}, journal={Annals of Applied Probability}, year={2016}, volume={26}, pages={3754-3785} }

We consider two dimensional Lotka-Volterra systems in fluctuating environment. Relying on recent results on stochastic persistence and piecewise deterministic Markov processes, we show that random switching between two environments both favorable to the same species can lead to the extinction of this species or coexistence of the species.

## 51 Citations

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

- Mathematics
- 2016

In this note, we study the long time behavior of Lotka-Volterra systems whose coefficients vary randomly. Bena{\"i}m and Lobry (2015) recently established that randomly switching between two…

### Lotka-Volterra with randomly fluctuating environments: a full description

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- 2016

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…

### Persistence in randomly switched Lotka-Volterra food chains

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- 2021

We consider a dynamical system obtained by the random switching between N Lotka-Volterra food chains. Our key assumption will be that at least two vector fields only differ on the resources allocated…

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Focusing on stochastic dynamics involving continuous states as well as discrete events, this paper investigates dynamical behaviors of stochastic multi-group Lotka-Volterra model with regime…

### Asymptotic Properties of Multi-species Lotka–Volterra Models with Regime Switching Involving Weak and Strong Interactions

- MathematicsJ. Nonlinear Sci.
- 2020

This work focuses on multi-species Lotka–Volterra models with regime switching modulated by a continuous-time Markov chain involving a small parameter, and obtains stochastic permanence and extinction using perturbed Lyapunov function methods.

### Persistence in Stochastic Lotka–Volterra Food Chains with Intraspecific Competition

- MathematicsBulletin of mathematical biology
- 2018

It is shown that one can classify, based on the invasion rates of the predators, which species go extinct and which converge to their unique invariant probability measure, and provides persistence/extinction criteria for food chains of length 4.

### Stochastic Lotka–Volterra food chains

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- 2018

It is shown that environmental stochasticity makes species more likely to go extinct, however, if the environmental fluctuations are small, persistence in the deterministic setting is preserved in the Stochastic system.

### Dynamic behavior of a stochastic predator-prey system under regime switching

- Mathematics
- 2017

A threshold is given by which to know whenever a switching predator-prey system is eventually extinct or permanent, and some numerical solutions are given to illustrate that under the regime switching, the permanence or extinction of the switching system may be very different from the dynamics in each fixed state.

### Strong stochastic persistence of some Lévy-driven Lotka–Volterra systems

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- 2022

It is proved that, under certain technical assumptions on the jump sizes and rates, there is convergence of the laws of the stochastic process to a unique stationary distribution supported far away from extinction.

### Persistence in the Moran model with random switching

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- 2019

The paper is devoted to the study of the asymptotic behaviour of Moran process in random environment, say random selection. In finite population, the Moran process may be degenerate in finite time,…

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