Stability and Coexistence of a Diffusive Predator-Prey System with Nonmonotonic Functional Response and Fear Effect
This paper investigates the diffusive predator-prey system with nonmonotonic functional response and fear effect. Firstly, we discussed the stability of the equilibrium solution for a corresponding ODE system. Secondly, we established a priori positive upper and lower bounds for the positive solutio...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/8899114 |
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| _version_ | 1832560312632475648 |
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| author | Xiaozhou Feng Hao Sun Yangfan Xiao Feng Xiao |
| author_facet | Xiaozhou Feng Hao Sun Yangfan Xiao Feng Xiao |
| author_sort | Xiaozhou Feng |
| collection | DOAJ |
| description | This paper investigates the diffusive predator-prey system with nonmonotonic functional response and fear effect. Firstly, we discussed the stability of the equilibrium solution for a corresponding ODE system. Secondly, we established a priori positive upper and lower bounds for the positive solutions of the PDE system. Thirdly, sufficient conditions for the local asymptotical stability of two positive equilibrium solutions of the system are given by using the method of eigenvalue spectrum analysis of linearization operator. Finally, the existence and nonexistence of nonconstant positive steady states of this reaction-diffusion system are established by the Leray–Schauder degree theory and Poincaré inequality. |
| format | Article |
| id | doaj-art-59687212329e42499483b4cf0550db8b |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-59687212329e42499483b4cf0550db8b2025-02-03T01:27:57ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/88991148899114Stability and Coexistence of a Diffusive Predator-Prey System with Nonmonotonic Functional Response and Fear EffectXiaozhou Feng0Hao Sun1Yangfan Xiao2Feng Xiao3College of Science, Xi’an Technological University, Xi’an 710032, ChinaCollege of Science, Xi’an Technological University, Xi’an 710032, ChinaCollege of Science, Xi’an Technological University, Xi’an 710032, ChinaCollege of Computer Science and Engineering, Xi’an Technological University, Xi’an 710032, ChinaThis paper investigates the diffusive predator-prey system with nonmonotonic functional response and fear effect. Firstly, we discussed the stability of the equilibrium solution for a corresponding ODE system. Secondly, we established a priori positive upper and lower bounds for the positive solutions of the PDE system. Thirdly, sufficient conditions for the local asymptotical stability of two positive equilibrium solutions of the system are given by using the method of eigenvalue spectrum analysis of linearization operator. Finally, the existence and nonexistence of nonconstant positive steady states of this reaction-diffusion system are established by the Leray–Schauder degree theory and Poincaré inequality.http://dx.doi.org/10.1155/2020/8899114 |
| spellingShingle | Xiaozhou Feng Hao Sun Yangfan Xiao Feng Xiao Stability and Coexistence of a Diffusive Predator-Prey System with Nonmonotonic Functional Response and Fear Effect Complexity |
| title | Stability and Coexistence of a Diffusive Predator-Prey System with Nonmonotonic Functional Response and Fear Effect |
| title_full | Stability and Coexistence of a Diffusive Predator-Prey System with Nonmonotonic Functional Response and Fear Effect |
| title_fullStr | Stability and Coexistence of a Diffusive Predator-Prey System with Nonmonotonic Functional Response and Fear Effect |
| title_full_unstemmed | Stability and Coexistence of a Diffusive Predator-Prey System with Nonmonotonic Functional Response and Fear Effect |
| title_short | Stability and Coexistence of a Diffusive Predator-Prey System with Nonmonotonic Functional Response and Fear Effect |
| title_sort | stability and coexistence of a diffusive predator prey system with nonmonotonic functional response and fear effect |
| url | http://dx.doi.org/10.1155/2020/8899114 |
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