Hopf Bifurcations and Oscillatory Patterns of a Homogeneous Reaction-Diffusion Singular Predator-Prey Model
A kind of homogeneous reaction-diffusion singular predator-prey model with no-flux boundary condition is considered. By using the abstract simplified Hopf bifurcation theorem due to Yi et al. 2009, we performed detailed Hopf bifurcation analysis of this particular pattern formation system. These res...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/547425 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832562499784802304 |
|---|---|
| author | Zhenhua Bao He Liu |
| author_facet | Zhenhua Bao He Liu |
| author_sort | Zhenhua Bao |
| collection | DOAJ |
| description | A kind of homogeneous reaction-diffusion singular predator-prey model with no-flux boundary condition is considered. By using the abstract simplified Hopf bifurcation theorem due to Yi et al. 2009, we performed detailed Hopf bifurcation analysis of this particular pattern formation system. These results suggest the existence of oscillatory patterns if the system parameters fall into certain parameter ranges. And all these oscillatory patterns are proved to be unstable. |
| format | Article |
| id | doaj-art-c25c132a6247408a9fdab4632ea0a17d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c25c132a6247408a9fdab4632ea0a17d2025-02-03T01:22:33ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/547425547425Hopf Bifurcations and Oscillatory Patterns of a Homogeneous Reaction-Diffusion Singular Predator-Prey ModelZhenhua Bao0He Liu1School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaSchool of Mathematics, Physics and Biological Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, ChinaA kind of homogeneous reaction-diffusion singular predator-prey model with no-flux boundary condition is considered. By using the abstract simplified Hopf bifurcation theorem due to Yi et al. 2009, we performed detailed Hopf bifurcation analysis of this particular pattern formation system. These results suggest the existence of oscillatory patterns if the system parameters fall into certain parameter ranges. And all these oscillatory patterns are proved to be unstable.http://dx.doi.org/10.1155/2013/547425 |
| spellingShingle | Zhenhua Bao He Liu Hopf Bifurcations and Oscillatory Patterns of a Homogeneous Reaction-Diffusion Singular Predator-Prey Model Abstract and Applied Analysis |
| title | Hopf Bifurcations and Oscillatory Patterns of a Homogeneous
Reaction-Diffusion Singular Predator-Prey Model |
| title_full | Hopf Bifurcations and Oscillatory Patterns of a Homogeneous
Reaction-Diffusion Singular Predator-Prey Model |
| title_fullStr | Hopf Bifurcations and Oscillatory Patterns of a Homogeneous
Reaction-Diffusion Singular Predator-Prey Model |
| title_full_unstemmed | Hopf Bifurcations and Oscillatory Patterns of a Homogeneous
Reaction-Diffusion Singular Predator-Prey Model |
| title_short | Hopf Bifurcations and Oscillatory Patterns of a Homogeneous
Reaction-Diffusion Singular Predator-Prey Model |
| title_sort | hopf bifurcations and oscillatory patterns of a homogeneous reaction diffusion singular predator prey model |
| url | http://dx.doi.org/10.1155/2013/547425 |
| work_keys_str_mv | AT zhenhuabao hopfbifurcationsandoscillatorypatternsofahomogeneousreactiondiffusionsingularpredatorpreymodel AT heliu hopfbifurcationsandoscillatorypatternsofahomogeneousreactiondiffusionsingularpredatorpreymodel |