# American Institute of Mathematical Sciences

2014, 11(2): 167-188. doi: 10.3934/mbe.2014.11.167

## A non-autonomous stochastic predator-prey model

 1 Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli, Italy, Italy, Italy 2 Dipartimento di Studi e Ricerche Aziendali, (Management & Information Technology), Università di Salerno, Via Ponte don Melillo, 84084 Fisciano (SA), Italy

Received  September 2012 Revised  January 2013 Published  October 2013

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. Mathematical Biosciences & Engineering, 2014, 11 (2) : 167-188. doi: 10.3934/mbe.2014.11.167
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