Conditions for permanence and ergodicity of certain stochastic predator–prey models
Copyright policy )Conditions for permanence and ergodicity of certain stochastic predator–prey models
Abstract In this paper we derive sufficient conditions for the permanence and ergodicity of a stochastic predator–prey model with a Beddington–DeAngelis functional response. The conditions obtained are in fact very close to the necessary conditions. Both nondegenerate and degenerate diffusions are considered. One of the distinctive features of our results is that they enable the characterization of the support of a unique invariant probability measure. It proves the convergence in total variation norm of the transition probability to the invariant measure. Comparisons to the existing literature and matters related to other stochastic predator–prey models are also given.
- Wayne State University United States
- Wayne State College United States
- Hanoi National University of Education Viet Nam
Ordinary differential equations and systems with randomness, extinction, Ergodicity, Probability (math.PR), Ergodicity, mixing, rates of mixing, 92D25, Asymptotic properties of solutions to ordinary differential equations, 34C12, Stochastic ordinary differential equations (aspects of stochastic analysis), stationary distribution, 34C12, 60H10, 92D25, Population dynamics (general), Qualitative investigation and simulation of ordinary differential equation models, FOS: Mathematics, ergodicity, Beddington-DeAngelis functional response, 60H10, predator-prey, permanence, Mathematics - Probability
Ordinary differential equations and systems with randomness, extinction, Ergodicity, Probability (math.PR), Ergodicity, mixing, rates of mixing, 92D25, Asymptotic properties of solutions to ordinary differential equations, 34C12, Stochastic ordinary differential equations (aspects of stochastic analysis), stationary distribution, 34C12, 60H10, 92D25, Population dynamics (general), Qualitative investigation and simulation of ordinary differential equation models, FOS: Mathematics, ergodicity, Beddington-DeAngelis functional response, 60H10, predator-prey, permanence, Mathematics - Probability
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