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| The Dynamics of Stochastic Predator-prey Modelswith Non-constant Mortality Rate and GeneralNonlinear Functional Response |
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| KeyWord:Stochastic predator-prey model Non-constant mortality rate Gen-
eral nonlinear functional response Extinction Stationary distribution |
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| Abstract: |
| In this paper, we investigate the dynamics of stochastic predator-
prey models with non-constant mortality rate and general nonlinear functional
response. For the stochastic system, we firstly prove the existence of the global
unique positive solution. Secondly, we establish sufficient conditions for the
extinction and persistence in the mean of autonomous stochastic model and
obtain a critical value between them. Then by constructing a appropriate
Lyapunov function, we prove that there exists a unique stationary distribution
and it has ergodicity in the case of persistence. Finally, numerical simulations
are introduced to illustrate our theoretical results. |
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