Almost Periodic Solution for an Epidemic Prey-Predator System with Impulsive Effects and Multiple Delays

Almost Periodic Solution for an Epidemic Prey-Predator System with Impulsive Effects and Multiple Delays

A nonautonomous epidemic prey-predator system with impulsive effects and multiple delays is considered; further, there is an epidemic disease in the predator. By the mean-value theorem of multiple variables, integral inequalities, differential inequalities, and other mathematical analysis skills, su...

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Main Authors: Baodan Tian, Ning Chen, Yanhong Qiu
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2015/486463
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spelling doaj-89aed75f41a940959979bca8970b90f42020-11-25T00:38:23ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/486463486463Almost Periodic Solution for an Epidemic Prey-Predator System with Impulsive Effects and Multiple DelaysBaodan Tian0Ning Chen1Yanhong Qiu2School of Science, Southwest University of Science and Technology, Mianyang 621010, ChinaSchool of Science, Southwest University of Science and Technology, Mianyang 621010, ChinaSchool of Science, Southwest University of Science and Technology, Mianyang 621010, ChinaA nonautonomous epidemic prey-predator system with impulsive effects and multiple delays is considered; further, there is an epidemic disease in the predator. By the mean-value theorem of multiple variables, integral inequalities, differential inequalities, and other mathematical analysis skills, sufficient conditions which guarantee the permanence of the system are obtained. Furthermore, by constructing a series of Lyapunov functionals it is proved that there exists a unique uniformly asymptotically stable almost periodic solution of the system.http://dx.doi.org/10.1155/2015/486463
collection DOAJ
language English
format Article
sources DOAJ
author Baodan Tian
Ning Chen
Yanhong Qiu
spellingShingle Baodan Tian
Ning Chen
Yanhong Qiu
Almost Periodic Solution for an Epidemic Prey-Predator System with Impulsive Effects and Multiple Delays
Discrete Dynamics in Nature and Society
author_facet Baodan Tian
Ning Chen
Yanhong Qiu
author_sort Baodan Tian
title Almost Periodic Solution for an Epidemic Prey-Predator System with Impulsive Effects and Multiple Delays
title_short Almost Periodic Solution for an Epidemic Prey-Predator System with Impulsive Effects and Multiple Delays
title_full Almost Periodic Solution for an Epidemic Prey-Predator System with Impulsive Effects and Multiple Delays
title_fullStr Almost Periodic Solution for an Epidemic Prey-Predator System with Impulsive Effects and Multiple Delays
title_full_unstemmed Almost Periodic Solution for an Epidemic Prey-Predator System with Impulsive Effects and Multiple Delays
title_sort almost periodic solution for an epidemic prey-predator system with impulsive effects and multiple delays
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2015-01-01
description A nonautonomous epidemic prey-predator system with impulsive effects and multiple delays is considered; further, there is an epidemic disease in the predator. By the mean-value theorem of multiple variables, integral inequalities, differential inequalities, and other mathematical analysis skills, sufficient conditions which guarantee the permanence of the system are obtained. Furthermore, by constructing a series of Lyapunov functionals it is proved that there exists a unique uniformly asymptotically stable almost periodic solution of the system.
url http://dx.doi.org/10.1155/2015/486463
work_keys_str_mv AT baodantian almostperiodicsolutionforanepidemicpreypredatorsystemwithimpulsiveeffectsandmultipledelays
AT ningchen almostperiodicsolutionforanepidemicpreypredatorsystemwithimpulsiveeffectsandmultipledelays
AT yanhongqiu almostperiodicsolutionforanepidemicpreypredatorsystemwithimpulsiveeffectsandmultipledelays
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