Stationary distribution and extinction of a stochastic predator–prey model with additional food and nonlinear perturbation

Qun Liu, Daqing Jiang, Tasawar Hayat and Bashir Ahmad

Applied Mathematics and Computation, 2018, vol. 320, issue C, 226-239

Abstract: In this paper, we formulate and analyze a stochastic predator–prey model with additional food and nonlinear perturbation. Firstly, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence of an ergodic stationary distribution of the positive solution to the model. Then we obtain sufficient conditions for extinction of the predator species in two cases, one is the prey species surviving and the predator species extinction; the other is both the prey and predator species are extinct. Finally, some examples together with numerical simulations are provided to illustrate the analytical results.

Keywords: Stochastic predator–prey model; Stationary distribution and ergodicity; Extinction; Habitat complexity; Additional food; Nonlinear perturbation (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (29)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:320:y:2018:i:c:p:226-239

DOI: 10.1016/j.amc.2017.09.030

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