Global Bifurcation Structure of a Predator-Prey System with a Spatial Degeneracy and B-D Functional Response
In this paper, we investigate a predator-prey system with Beddington–DeAngelis (B-D) functional response in a spatially degenerate heterogeneous environment. First, for the case of the weak growth rate on the prey (λ1Ω<a<λ1Ω0), a priori estimates on any positive steady-state solutions are esta...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/9970255 |
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| author | Xiaozhou Feng Changtong Li Hao Sun Yuzhen Wang |
| author_facet | Xiaozhou Feng Changtong Li Hao Sun Yuzhen Wang |
| author_sort | Xiaozhou Feng |
| collection | DOAJ |
| description | In this paper, we investigate a predator-prey system with Beddington–DeAngelis (B-D) functional response in a spatially degenerate heterogeneous environment. First, for the case of the weak growth rate on the prey (λ1Ω<a<λ1Ω0), a priori estimates on any positive steady-state solutions are established by the comparison principle; two local bifurcation solution branches depending on the bifurcation parameter are obtained by local bifurcation theory. Moreover, the demonstrated two local bifurcation solution branches can be extended to a bounded global bifurcation curve by the global bifurcation theory. Second, for the case of the strong growth rate on the prey (a>λ1Ω0), a priori estimates on any positive steady-state solutions are obtained by applying reduction to absurdity and the set of positive steady-state solutions forms an unbounded global bifurcation curve by the global bifurcation theory. In the end, discussions on the difference of the solution properties between the traditional predator-prey system and the predator-prey system with a spatial degeneracy and B-D functional response are addressed. |
| format | Article |
| id | doaj-art-43e746bfcd214671b112e1191dfbd179 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-43e746bfcd214671b112e1191dfbd1792025-02-03T01:27:08ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/99702559970255Global Bifurcation Structure of a Predator-Prey System with a Spatial Degeneracy and B-D Functional ResponseXiaozhou Feng0Changtong Li1Hao Sun2Yuzhen Wang3School of Science, Xi’an Technological University, Xi’an 710032, ChinaSchool of Science, Xi’an Technological University, Xi’an 710032, ChinaSchool of Science, Xi’an Technological University, Xi’an 710032, ChinaSchool of Science, Xi’an Technological University, Xi’an 710032, ChinaIn this paper, we investigate a predator-prey system with Beddington–DeAngelis (B-D) functional response in a spatially degenerate heterogeneous environment. First, for the case of the weak growth rate on the prey (λ1Ω<a<λ1Ω0), a priori estimates on any positive steady-state solutions are established by the comparison principle; two local bifurcation solution branches depending on the bifurcation parameter are obtained by local bifurcation theory. Moreover, the demonstrated two local bifurcation solution branches can be extended to a bounded global bifurcation curve by the global bifurcation theory. Second, for the case of the strong growth rate on the prey (a>λ1Ω0), a priori estimates on any positive steady-state solutions are obtained by applying reduction to absurdity and the set of positive steady-state solutions forms an unbounded global bifurcation curve by the global bifurcation theory. In the end, discussions on the difference of the solution properties between the traditional predator-prey system and the predator-prey system with a spatial degeneracy and B-D functional response are addressed.http://dx.doi.org/10.1155/2021/9970255 |
| spellingShingle | Xiaozhou Feng Changtong Li Hao Sun Yuzhen Wang Global Bifurcation Structure of a Predator-Prey System with a Spatial Degeneracy and B-D Functional Response Complexity |
| title | Global Bifurcation Structure of a Predator-Prey System with a Spatial Degeneracy and B-D Functional Response |
| title_full | Global Bifurcation Structure of a Predator-Prey System with a Spatial Degeneracy and B-D Functional Response |
| title_fullStr | Global Bifurcation Structure of a Predator-Prey System with a Spatial Degeneracy and B-D Functional Response |
| title_full_unstemmed | Global Bifurcation Structure of a Predator-Prey System with a Spatial Degeneracy and B-D Functional Response |
| title_short | Global Bifurcation Structure of a Predator-Prey System with a Spatial Degeneracy and B-D Functional Response |
| title_sort | global bifurcation structure of a predator prey system with a spatial degeneracy and b d functional response |
| url | http://dx.doi.org/10.1155/2021/9970255 |
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