Dynamical Behavior of a Predator-Prey System Incorporating a Prey Refuge with Impulse Effect

A predator-prey model with Holling II functional response incorporating a prey refuge with impulse effect is considered in this paper. With the help of the Floquet theory of impulsive differential equations, local stability and global attractivity of the boundary periodic solution of the system are...

Full description

Saved in:
Bibliographic Details
Main Authors: Zuxiong Li, Xue Yang, Shengnan Fu
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2022/2422923
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1832558293155840000
author Zuxiong Li
Xue Yang
Shengnan Fu
author_facet Zuxiong Li
Xue Yang
Shengnan Fu
author_sort Zuxiong Li
collection DOAJ
description A predator-prey model with Holling II functional response incorporating a prey refuge with impulse effect is considered in this paper. With the help of the Floquet theory of impulsive differential equations, local stability and global attractivity of the boundary periodic solution of the system are derived, and then sufficient conditions for global asymptotic stability of the boundary periodic solution are obtained. Next, the permanence of the system is proved by constructing a Lyapunov function. Further, by applying the bifurcation theory of impulsive differential equations, conditions under which the system has a positive periodic solution are obtained. Finally, numerical simulations are presented to illustrate the analytical results.
format Article
id doaj-art-13add66a0c5a40a5b1caf866d05ffec0
institution Kabale University
issn 1099-0526
language English
publishDate 2022-01-01
publisher Wiley
record_format Article
series Complexity
spelling doaj-art-13add66a0c5a40a5b1caf866d05ffec02025-02-03T01:32:41ZengWileyComplexity1099-05262022-01-01202210.1155/2022/2422923Dynamical Behavior of a Predator-Prey System Incorporating a Prey Refuge with Impulse EffectZuxiong Li0Xue Yang1Shengnan Fu2College of Mathematics and StatisticsHuji Senior Middle School Zhong XiangGuangzhou Huangpu District (Development Zone) Taxation BureauA predator-prey model with Holling II functional response incorporating a prey refuge with impulse effect is considered in this paper. With the help of the Floquet theory of impulsive differential equations, local stability and global attractivity of the boundary periodic solution of the system are derived, and then sufficient conditions for global asymptotic stability of the boundary periodic solution are obtained. Next, the permanence of the system is proved by constructing a Lyapunov function. Further, by applying the bifurcation theory of impulsive differential equations, conditions under which the system has a positive periodic solution are obtained. Finally, numerical simulations are presented to illustrate the analytical results.http://dx.doi.org/10.1155/2022/2422923
spellingShingle Zuxiong Li
Xue Yang
Shengnan Fu
Dynamical Behavior of a Predator-Prey System Incorporating a Prey Refuge with Impulse Effect
Complexity
title Dynamical Behavior of a Predator-Prey System Incorporating a Prey Refuge with Impulse Effect
title_full Dynamical Behavior of a Predator-Prey System Incorporating a Prey Refuge with Impulse Effect
title_fullStr Dynamical Behavior of a Predator-Prey System Incorporating a Prey Refuge with Impulse Effect
title_full_unstemmed Dynamical Behavior of a Predator-Prey System Incorporating a Prey Refuge with Impulse Effect
title_short Dynamical Behavior of a Predator-Prey System Incorporating a Prey Refuge with Impulse Effect
title_sort dynamical behavior of a predator prey system incorporating a prey refuge with impulse effect
url http://dx.doi.org/10.1155/2022/2422923
work_keys_str_mv AT zuxiongli dynamicalbehaviorofapredatorpreysystemincorporatingapreyrefugewithimpulseeffect
AT xueyang dynamicalbehaviorofapredatorpreysystemincorporatingapreyrefugewithimpulseeffect
AT shengnanfu dynamicalbehaviorofapredatorpreysystemincorporatingapreyrefugewithimpulseeffect