Complex Dynamics of a Stochastic Two-Patch Predator-Prey Population Model with Ratio-Dependent Functional Responses
This 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. Then, two different methods are used to discuss the long-time properties of the sol...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/6671499 |
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| _version_ | 1832550537482993664 |
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| author | Rong Liu Guirong Liu |
| author_facet | Rong Liu Guirong Liu |
| author_sort | Rong Liu |
| collection | DOAJ |
| description | This 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. Then, 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. The results in this paper generalize and improve the previous related results. |
| format | Article |
| id | doaj-art-194d1138f0ba4027ab64ee4f2287bcfb |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-194d1138f0ba4027ab64ee4f2287bcfb2025-02-03T06:06:30ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/66714996671499Complex Dynamics of a Stochastic Two-Patch Predator-Prey Population Model with Ratio-Dependent Functional ResponsesRong Liu0Guirong Liu1School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, Shanxi 030006, ChinaSchool of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, ChinaThis 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. Then, 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. The results in this paper generalize and improve the previous related results.http://dx.doi.org/10.1155/2021/6671499 |
| spellingShingle | Rong Liu Guirong Liu Complex Dynamics of a Stochastic Two-Patch Predator-Prey Population Model with Ratio-Dependent Functional Responses Complexity |
| title | Complex Dynamics of a Stochastic Two-Patch Predator-Prey Population Model with Ratio-Dependent Functional Responses |
| title_full | Complex Dynamics of a Stochastic Two-Patch Predator-Prey Population Model with Ratio-Dependent Functional Responses |
| title_fullStr | Complex Dynamics of a Stochastic Two-Patch Predator-Prey Population Model with Ratio-Dependent Functional Responses |
| title_full_unstemmed | Complex Dynamics of a Stochastic Two-Patch Predator-Prey Population Model with Ratio-Dependent Functional Responses |
| title_short | Complex Dynamics of a Stochastic Two-Patch Predator-Prey Population Model with Ratio-Dependent Functional Responses |
| title_sort | complex dynamics of a stochastic two patch predator prey population model with ratio dependent functional responses |
| url | http://dx.doi.org/10.1155/2021/6671499 |
| work_keys_str_mv | AT rongliu complexdynamicsofastochastictwopatchpredatorpreypopulationmodelwithratiodependentfunctionalresponses AT guirongliu complexdynamicsofastochastictwopatchpredatorpreypopulationmodelwithratiodependentfunctionalresponses |