Global stability for a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge
Abstract In this paper, a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge is proposed. Applying the comparison theory of differential equation, sufficient average criteria on the permanence of solutions and the existence of the pos...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-03-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02563-7 |
| _version_ | 1818303335952809984 |
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| author | Yantao Luo Long Zhang Zhidong Teng Tingting Zheng |
| author_facet | Yantao Luo Long Zhang Zhidong Teng Tingting Zheng |
| author_sort | Yantao Luo |
| collection | DOAJ |
| description | Abstract In this paper, a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge is proposed. Applying the comparison theory of differential equation, sufficient average criteria on the permanence of solutions and the existence of the positive periodic solutions are established. Moreover, the existence region of the positive periodic solutions is an invariant region dependent on t. Then, constructing a suitable Lyapunov function, we obtain sufficient conditions to guarantee the global asymptotic stability of the positive periodic solutions. Finally, we do some numerical simulations to verify our main results and investigate the effect of prey refuge on the dynamics of the system. |
| first_indexed | 2024-12-13T05:53:10Z |
| format | Article |
| id | doaj.art-9d6619eb6c444b208a74c9f4af717cb7 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-13T05:53:10Z |
| publishDate | 2020-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-9d6619eb6c444b208a74c9f4af717cb72022-12-21T23:57:30ZengSpringerOpenAdvances in Difference Equations1687-18472020-03-012020111610.1186/s13662-020-02563-7Global stability for a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refugeYantao Luo0Long Zhang1Zhidong Teng2Tingting Zheng3College of Mathematics and System Sciences, Xinjiang UniversityCollege of Mathematics and System Sciences, Xinjiang UniversityCollege of Mathematics and System Sciences, Xinjiang UniversityCollege of Mathematics and System Sciences, Xinjiang UniversityAbstract In this paper, a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge is proposed. Applying the comparison theory of differential equation, sufficient average criteria on the permanence of solutions and the existence of the positive periodic solutions are established. Moreover, the existence region of the positive periodic solutions is an invariant region dependent on t. Then, constructing a suitable Lyapunov function, we obtain sufficient conditions to guarantee the global asymptotic stability of the positive periodic solutions. Finally, we do some numerical simulations to verify our main results and investigate the effect of prey refuge on the dynamics of the system.http://link.springer.com/article/10.1186/s13662-020-02563-7NonautonomousReaction-diffusionModified Leslie–GowerPredator-preyGlobal asymptotic stability |
| spellingShingle | Yantao Luo Long Zhang Zhidong Teng Tingting Zheng Global stability for a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge Advances in Difference Equations Nonautonomous Reaction-diffusion Modified Leslie–Gower Predator-prey Global asymptotic stability |
| title | Global stability for a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge |
| title_full | Global stability for a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge |
| title_fullStr | Global stability for a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge |
| title_full_unstemmed | Global stability for a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge |
| title_short | Global stability for a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge |
| title_sort | global stability for a nonautonomous reaction diffusion predator prey model with modified leslie gower holling ii schemes and a prey refuge |
| topic | Nonautonomous Reaction-diffusion Modified Leslie–Gower Predator-prey Global asymptotic stability |
| url | http://link.springer.com/article/10.1186/s13662-020-02563-7 |
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