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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 λ 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[J]. Mathematical Biosciences and Engineering, 2009, 6(4): 683-700. doi: 10.3934/mbe.2009.6.683

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  • 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 λ which is useful to make suitable predictions about the persistence of the system.


  • This article has been cited by:

    1. Nguyen Huu Du, Nguyen Hai Dang, Asymptotic behavior of Kolmogorov systems with predator-prey type in random environment, 2014, 13, 1534-0392, 2693, 10.3934/cpaa.2014.13.2693
    2. XINYU BO, GUANGYING LV, WENJUN LIU, ALI MOUSSAOUI, OPTIMAL HARVEST CONTROL OF PREDATOR–PREY SYSTEMS IN FISHERIES WITH STAGE STRUCTURE AND ADDITIONAL FOOD SUPPLY, 2025, 33, 0218-3390, 221, 10.1142/S0218339025500032
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  • © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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