Rich dynamics of a stochastic Michaelis–Menten-type ratio-dependent predator–prey system

Chunyan Ji, Daqing Jiang and Jing Fu

Physica A: Statistical Mechanics and its Applications, 2019, vol. 526, issue C

Abstract: Stochastic predator–prey systems with different functional responses have been studied. But the dynamics of a Michaelis–Menten-type ratio-dependent predator–prey system with stochastic perturbation is not investigated systematically. In this paper, we give the asymptotic behavior of this system. Sufficient criteria for the existence of a stationary distribution and ergodicity are obtained, which means the species are permanent. Besides, we show the situations in which the species are non-persistence. Finally, examples and simulations are carried on to verify these results.

Keywords: Stochastic ratio-dependent predator–prey system; Stationary distribution; Ergodicity; Non-persistence; Extinction (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:526:y:2019:i:c:s0378437119304236

DOI: 10.1016/j.physa.2019.04.039

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