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Ergodicity and threshold behaviors of a predator‐prey model in stochastic chemostat driven by regime switching
Author(s) -
Wang Liang,
Jiang Daqing
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6738
Subject(s) - chemostat , extinction (optical mineralogy) , mathematics , ergodicity , stationary distribution , predation , statistical physics , markov chain , predator , control theory (sociology) , stochastic modelling , mathematical optimization , ecology , statistics , biology , computer science , physics , paleontology , genetics , control (management) , artificial intelligence , bacteria
This paper deals with a stochastic predator‐prey model in chemostat which is driven by Markov regime switching. For the asymptotic behaviors of this stochastic system, we establish the sufficient conditions for the existence of the stationary distribution. Then, we investigate, respectively, the extinction of the prey and predator populations. We explore the new critical numbers between survival and extinction for species of the dual‐threshold chemostat model. Numerical simulations are accomplished to confirm our analytical conclusions.