# American Institute of Mathematical Sciences

2009, 6(4): 683-700. doi: 10.3934/mbe.2009.6.683

## Evolution of Lotka-Volterra predator-prey systems under telegraph noise

 1 IRD, UMI 209, UMMISCO, IRD France Nord, F-93143, Bondy, France 2 Faculty of Mathematics, Mechanics and Informatics, Vietnam National University, Hanoi, Vietnam, Vietnam

Received  April 2009 Revised  June 2009 Published  September 2009

In this paper we study a Lotka-Volterra predator-prey system with prey logistic growth under the telegraph noise. The telegraph noise switches at random two prey-predator models. The aim of this work is to determine the subset of omega-limit set of the system and show out the existence of a stationary distribution. We also focus on persistence of the predator and thus we look for conditions that allow persistence of the predator and prey community. We show that the asymptotic behaviour highly depends on the value of some constant $\lambda$ which is useful to make suitable predictions about the persistence of the system.
Citation: P. Auger, N. H. Du, N. T. Hieu. Evolution of Lotka-Volterra predator-prey systems under telegraph noise. Mathematical Biosciences & Engineering, 2009, 6 (4) : 683-700. doi: 10.3934/mbe.2009.6.683
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