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. 

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