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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Main Authors: Guirong Liu, Rong Liu
Format: Article
Language:English
Published: Wiley 2019-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2019/4876165
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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.
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publishDate 2019-01-01
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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