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

P. Auger; N. H. Du; N. T. Hieu; P. Auger; N. H. Du; N. T. Hieu

doi:10.3934/mbe.2009.6.683

Mathematical Biosciences and Engineering

2009, Volume 6, Issue 4: 683-700. doi: 10.3934/mbe.2009.6.683

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

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

Received: 01 April 2009 Accepted: 29 June 2018 Published: 01 September 2009
MSC : 34C12, 60H10, 92D25.

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.
- carrying capacity,
- telegraph noise,
- stationary distribution.,
- Lotka-Volterra predator-prey systems
Citation: P. Auger, N. H. Du, N. T. Hieu. Evolution of Lotka-Volterra predator-prey systems under telegraph noise[J]. Mathematical Biosciences and Engineering, 2009, 6(4): 683-700. doi: 10.3934/mbe.2009.6.683

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Abstract

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.
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