Lotka Volterra in fluctuating environment or "how switching between   beneficial environments can make survival harder"
  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. 
Michel Bena\"im and Claude Lobry
math.PR math.DS