Dynamics of a stochastic Markovian switching predator–prey model with infinite memory and general Lévy jumps

Chun Lu

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 181, issue C, 316-332

Abstract: This paper investigates a stochastic Markovian switching predator–prey model with infinite memory and general Lévy jumps. Firstly, we transfer a classic infinite memory predator–prey model with weak kernel case into an equivalent model through integral transform. Then, for the corresponding stochastic Markovian switching model, we establish the sufficient conditions for permanence in time average and the threshold between stability in time average and extinction. Finally, sufficient criteria for a unique ergodic stationary distribution of the model are derived. Our results show that, firstly, both white noise and infinite memory are unfavorable to the existence of the stationary distribution; secondly, the general Lévy jumps could make the stationary distribution vanish as well as happen; finally, the Markovian switching could make the stationary distribution appear.

Keywords: Infinite memory predator–prey model; Stationary distribution; Permanence in time average; General Lévy jumps; Markovian switching (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:181:y:2021:i:c:p:316-332

DOI: 10.1016/j.matcom.2020.10.002

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