Complex Dynamics of a Stochastic Two-Patch Predator-Prey Population Model with Ratio-Dependent Functional Responses | Zendy

Rong Liu | Zendy; Guirong Liu | Zendy

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Complex Dynamics of a Stochastic Two-Patch Predator-Prey Population Model with Ratio-Dependent Functional Responses

Author(s) -

Rong Liu,

Guirong Liu

Publication year - 2021

Publication title -

complexity

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.447

H-Index - 61

eISSN - 1099-0526

pISSN - 1076-2787

DOI - 10.1155/2021/6671499

Subject(s) - ergodic theory , functional response , mathematics , stationary distribution , extinction (optical mineralogy) , lyapunov function , persistence (discontinuity) , dynamics (music) , stochastic dynamics , population , predation , statistical physics , mathematical optimization , predator , mathematical analysis , ecology , statistics , nonlinear system , markov chain , physics , quantum mechanics , sociology , acoustics , biology , engineering , demography , geotechnical engineering , optics

*is paper investigates a stochastic two-patch predator-prey model with ratio-dependent functional responses. First, the existence of a unique global positive solution is proved via the stochastic comparison theorem. *en, two different methods are used to discuss the long-time properties of the solutions pathwise. Next, sufficient conditions for extinction and persistence in mean are obtained. Moreover, stochastic persistence of the model is discussed. Furthermore, sufficient conditions for the existence of an ergodic stationary distribution are derived by a suitable Lyapunov function. Next, we apply the main results in some special models. Finally, some numerical simulations are introduced to support the main results obtained. *e results in this paper generalize and improve the previous related results.

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