Dynamics of Mutualism-Competition-Predator System with Beddington-DeAngelis Functional Responses and Impulsive Perturbations

Dynamics of Mutualism-Competition-Predator System with Beddington-DeAngelis Functional Responses and Impulsive Perturbations

We explore the dynamics of a class of mutualism-competition-predator interaction models with Beddington-DeAngelis functional responses and impulsive perturbations. Sufficient conditions for existence of positive periodic solution are established by using a continuation theorem in coincidence degree...

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Main Authors: Xiaoming Fan, Zhigang Wang, Fuquan Jiang
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/963486
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spelling doaj-f5898f971f5a4dd2ad6efc2d15937fb62020-11-25T00:07:53ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/963486963486Dynamics of Mutualism-Competition-Predator System with Beddington-DeAngelis Functional Responses and Impulsive PerturbationsXiaoming Fan0Zhigang Wang1Fuquan Jiang2School of Mathematics Science, Harbin Normal University, Harbin 150500, ChinaSchool of Mathematics Science, Harbin Normal University, Harbin 150500, ChinaFoundation Department, Harbin Finance University, Harbin 150030, ChinaWe explore the dynamics of a class of mutualism-competition-predator interaction models with Beddington-DeAngelis functional responses and impulsive perturbations. Sufficient conditions for existence of positive periodic solution are established by using a continuation theorem in coincidence degree theory, which have been extensively applied in studying existence problems in differential equations and difference equations. In addition, sufficient criteria are given for the global stability and the globally exponential stability of system by employing comparison principle and Lyapunov method.http://dx.doi.org/10.1155/2012/963486
collection DOAJ
language English
format Article
sources DOAJ
author Xiaoming Fan
Zhigang Wang
Fuquan Jiang
spellingShingle Xiaoming Fan
Zhigang Wang
Fuquan Jiang
Dynamics of Mutualism-Competition-Predator System with Beddington-DeAngelis Functional Responses and Impulsive Perturbations
Abstract and Applied Analysis
author_facet Xiaoming Fan
Zhigang Wang
Fuquan Jiang
author_sort Xiaoming Fan
title Dynamics of Mutualism-Competition-Predator System with Beddington-DeAngelis Functional Responses and Impulsive Perturbations
title_short Dynamics of Mutualism-Competition-Predator System with Beddington-DeAngelis Functional Responses and Impulsive Perturbations
title_full Dynamics of Mutualism-Competition-Predator System with Beddington-DeAngelis Functional Responses and Impulsive Perturbations
title_fullStr Dynamics of Mutualism-Competition-Predator System with Beddington-DeAngelis Functional Responses and Impulsive Perturbations
title_full_unstemmed Dynamics of Mutualism-Competition-Predator System with Beddington-DeAngelis Functional Responses and Impulsive Perturbations
title_sort dynamics of mutualism-competition-predator system with beddington-deangelis functional responses and impulsive perturbations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description We explore the dynamics of a class of mutualism-competition-predator interaction models with Beddington-DeAngelis functional responses and impulsive perturbations. Sufficient conditions for existence of positive periodic solution are established by using a continuation theorem in coincidence degree theory, which have been extensively applied in studying existence problems in differential equations and difference equations. In addition, sufficient criteria are given for the global stability and the globally exponential stability of system by employing comparison principle and Lyapunov method.
url http://dx.doi.org/10.1155/2012/963486
work_keys_str_mv AT xiaomingfan dynamicsofmutualismcompetitionpredatorsystemwithbeddingtondeangelisfunctionalresponsesandimpulsiveperturbations
AT zhigangwang dynamicsofmutualismcompetitionpredatorsystemwithbeddingtondeangelisfunctionalresponsesandimpulsiveperturbations
AT fuquanjiang dynamicsofmutualismcompetitionpredatorsystemwithbeddingtondeangelisfunctionalresponsesandimpulsiveperturbations
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