Dynamics of a Stochastic Three-Species Food Web Model with Omnivory and Ratio-Dependent Functional Response
This paper is concerned with a stochastic three-species food web model with omnivory which is defined as feeding on more than one trophic level. The model involves a prey, an intermediate predator, and an omnivorous top predator. First, by the stochastic comparison theorem, we show that there is a u...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/4876165 |
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| _version_ | 1849686044785508352 |
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| author | Guirong Liu Rong Liu |
| author_facet | Guirong Liu Rong Liu |
| author_sort | Guirong Liu |
| collection | DOAJ |
| description | This paper is concerned with a stochastic three-species food web model with omnivory which is defined as feeding on more than one trophic level. The model involves a prey, an intermediate predator, and an omnivorous top predator. First, by the stochastic comparison theorem, we show that there is a unique global positive solution to the model. Next, we investigate the asymptotic pathwise behavior of the model. Then, we conclude that the model is persistent in mean and extinct and discuss the stochastic persistence of the model. Further, by constructing a suitable Lyapunov function, we establish sufficient conditions for the existence of an ergodic stationary distribution to the model. Then, we present the application of the main results in some special models. Finally, we introduce some numerical simulations to support the main results obtained. The results in this paper generalize and improve the previous related results. |
| format | Article |
| id | doaj-art-b914efe8b4004fe2ba389e514f30d4da |
| institution | DOAJ |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-b914efe8b4004fe2ba389e514f30d4da2025-08-20T03:22:50ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/48761654876165Dynamics of a Stochastic Three-Species Food Web Model with Omnivory and Ratio-Dependent Functional ResponseGuirong Liu0Rong Liu1School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, ChinaSchool of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, Shanxi 030006, ChinaThis paper is concerned with a stochastic three-species food web model with omnivory which is defined as feeding on more than one trophic level. The model involves a prey, an intermediate predator, and an omnivorous top predator. First, by the stochastic comparison theorem, we show that there is a unique global positive solution to the model. Next, we investigate the asymptotic pathwise behavior of the model. Then, we conclude that the model is persistent in mean and extinct and discuss the stochastic persistence of the model. Further, by constructing a suitable Lyapunov function, we establish sufficient conditions for the existence of an ergodic stationary distribution to the model. Then, we present the application of the main results in some special models. Finally, we introduce some numerical simulations to support the main results obtained. The results in this paper generalize and improve the previous related results.http://dx.doi.org/10.1155/2019/4876165 |
| spellingShingle | Guirong Liu Rong Liu Dynamics of a Stochastic Three-Species Food Web Model with Omnivory and Ratio-Dependent Functional Response Complexity |
| title | Dynamics of a Stochastic Three-Species Food Web Model with Omnivory and Ratio-Dependent Functional Response |
| title_full | Dynamics of a Stochastic Three-Species Food Web Model with Omnivory and Ratio-Dependent Functional Response |
| title_fullStr | Dynamics of a Stochastic Three-Species Food Web Model with Omnivory and Ratio-Dependent Functional Response |
| title_full_unstemmed | Dynamics of a Stochastic Three-Species Food Web Model with Omnivory and Ratio-Dependent Functional Response |
| title_short | Dynamics of a Stochastic Three-Species Food Web Model with Omnivory and Ratio-Dependent Functional Response |
| title_sort | dynamics of a stochastic three species food web model with omnivory and ratio dependent functional response |
| url | http://dx.doi.org/10.1155/2019/4876165 |
| work_keys_str_mv | AT guirongliu dynamicsofastochasticthreespeciesfoodwebmodelwithomnivoryandratiodependentfunctionalresponse AT rongliu dynamicsofastochasticthreespeciesfoodwebmodelwithomnivoryandratiodependentfunctionalresponse |