Stationary distribution of a stochastic predator–prey model with distributed delay and general functional response

Qun Liu, Daqing Jiang, Xiuli He, Tasawar Hayat and Ahmed Alsaedi

Physica A: Statistical Mechanics and its Applications, 2019, vol. 513, issue C, 273-287

Abstract: In this paper, we study a stochastic predator–prey model with distributed delay and general functional response. We transform the model with weak kernel case into an equivalent system through the linear chain technique. Since the diffusion matrix is degenerate, the uniform ellipticity condition does not hold. The Markov semigroup theory is used to derive the existence of a unique stable stationary distribution. We verify the densities of the distributions of the positive solutions can converge in L1 to an invariant density.

Keywords: Stochastic predator–prey model; General functional response; Markov semigroups; Distributed delay; Stationary distribution (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:513:y:2019:i:c:p:273-287

DOI: 10.1016/j.physa.2018.09.033

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