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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/2422923 |
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| _version_ | 1832558293155840000 |
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| 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 |
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