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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 2: 167-188. doi: 10.3934/mbe.2014.11.167
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A non-autonomous stochastic predator-prey model

  • 1.
    Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli
  • 2.
    Dipartimento di Studi e Ricerche Aziendali, (Management & Information Technology), Università di Salerno, Via Ponte don Melillo, 84084 Fisciano (SA)
  • Received: 01 September 2012 Accepted: 29 June 2018 Published: 01 October 2013

  • MSC : Primary: 92D25, 60J60; Secondary: 60K37.

  • The aim of this paper is to consider a non-autonomous predator-prey-like system, with a Gompertz growth law for the prey.By introducing random variations in both prey birth and predator death rates,a stochastic model for the predator-prey-like system in a random environment is proposed and investigated.The corresponding Fokker-Planck equation is solved to obtain the joint probability density for the prey and predator populations and the marginal probability densities.The asymptotic behavior of the predator-prey stochastic model is also analyzed.

    Citation: Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Amelia G. Nobile. A non-autonomous stochastic predator-prey model[J]. Mathematical Biosciences and Engineering, 2014, 11(2): 167-188. doi: 10.3934/mbe.2014.11.167

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  • The aim of this paper is to consider a non-autonomous predator-prey-like system, with a Gompertz growth law for the prey.By introducing random variations in both prey birth and predator death rates,a stochastic model for the predator-prey-like system in a random environment is proposed and investigated.The corresponding Fokker-Planck equation is solved to obtain the joint probability density for the prey and predator populations and the marginal probability densities.The asymptotic behavior of the predator-prey stochastic model is also analyzed.


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