Global Dynamics of a Prey-Predator Model with Antipredator Behavior and Two Predators

Global Dynamics of a Prey-Predator Model with Antipredator Behavior and Two Predators

In this work, we establish a new model of one prey and two predators with antipredator behavior. The basic properties on the positivity and boundedness of solutions and the existence of equilibria are established. Through analyzing the global dynamics, we find that there exist some values of the par...

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Main Authors: Chentong Li, Yingying Zhang, Jinhu Xu, Yicang Zhou
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2019/3586508
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spelling doaj-a3c8228e75ea4f34a1f59bc5af67dbdc2020-11-25T02:17:20ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2019-01-01201910.1155/2019/35865083586508Global Dynamics of a Prey-Predator Model with Antipredator Behavior and Two PredatorsChentong Li0Yingying Zhang1Jinhu Xu2Yicang Zhou3School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaSchool of Sciences, Xi’an University of Technology, Xi’an, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaIn this work, we establish a new model of one prey and two predators with antipredator behavior. The basic properties on the positivity and boundedness of solutions and the existence of equilibria are established. Through analyzing the global dynamics, we find that there exist some values of the parameters such that one of the predators can be driven into being extinct by another. Furthermore, the coexistence of the three species is investigated which shows that the antipredator behavior makes the species coexist by periodic oscillation. The results give a new insight into the influence of antipredator behavior in nature selection.http://dx.doi.org/10.1155/2019/3586508
collection DOAJ
language English
format Article
sources DOAJ
author Chentong Li
Yingying Zhang
Jinhu Xu
Yicang Zhou
spellingShingle Chentong Li
Yingying Zhang
Jinhu Xu
Yicang Zhou
Global Dynamics of a Prey-Predator Model with Antipredator Behavior and Two Predators
Discrete Dynamics in Nature and Society
author_facet Chentong Li
Yingying Zhang
Jinhu Xu
Yicang Zhou
author_sort Chentong Li
title Global Dynamics of a Prey-Predator Model with Antipredator Behavior and Two Predators
title_short Global Dynamics of a Prey-Predator Model with Antipredator Behavior and Two Predators
title_full Global Dynamics of a Prey-Predator Model with Antipredator Behavior and Two Predators
title_fullStr Global Dynamics of a Prey-Predator Model with Antipredator Behavior and Two Predators
title_full_unstemmed Global Dynamics of a Prey-Predator Model with Antipredator Behavior and Two Predators
title_sort global dynamics of a prey-predator model with antipredator behavior and two predators
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2019-01-01
description In this work, we establish a new model of one prey and two predators with antipredator behavior. The basic properties on the positivity and boundedness of solutions and the existence of equilibria are established. Through analyzing the global dynamics, we find that there exist some values of the parameters such that one of the predators can be driven into being extinct by another. Furthermore, the coexistence of the three species is investigated which shows that the antipredator behavior makes the species coexist by periodic oscillation. The results give a new insight into the influence of antipredator behavior in nature selection.
url http://dx.doi.org/10.1155/2019/3586508
work_keys_str_mv AT chentongli globaldynamicsofapreypredatormodelwithantipredatorbehaviorandtwopredators
AT yingyingzhang globaldynamicsofapreypredatormodelwithantipredatorbehaviorandtwopredators
AT jinhuxu globaldynamicsofapreypredatormodelwithantipredatorbehaviorandtwopredators
AT yicangzhou globaldynamicsofapreypredatormodelwithantipredatorbehaviorandtwopredators
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