Dynamics of a Predator-Prey System with a Mate-Finding Allee Effect
We consider a ratio-dependent predator-prey system with a mate-finding Allee effect on prey. The stability properties of the equilibria and a complete bifurcation analysis, including the existence of a saddle-node, a Hopf bifurcation, and, a Bogdanov-Takens bifurcations, have been proved theoretical...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/673424 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832554732660457472 |
|---|---|
| author | Ruiwen Wu Xiuxiang Liu |
| author_facet | Ruiwen Wu Xiuxiang Liu |
| author_sort | Ruiwen Wu |
| collection | DOAJ |
| description | We consider a ratio-dependent predator-prey system with a mate-finding Allee effect on prey. The stability properties of the equilibria and a complete bifurcation analysis, including the existence of a saddle-node, a Hopf bifurcation, and, a Bogdanov-Takens bifurcations, have been proved theoretically and numerically. The blow-up method has been applied to investigate the structure of a neighborhood of the origin. Our mathematical results show the mate-finding Allee effect can reduce the complexity of system behaviors by making the complicated equilibrium less complicated, and it can be a destabilizing force as well, which makes the system has a high possibility of being threatened with extinction in ecology. |
| format | Article |
| id | doaj-art-c60c8abcfd97406bb78a9c46e10dfb54 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c60c8abcfd97406bb78a9c46e10dfb542025-02-03T05:50:42ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/673424673424Dynamics of a Predator-Prey System with a Mate-Finding Allee EffectRuiwen Wu0Xiuxiang Liu1School of Mathematical Sciences, South China Normal University, Guangzhou 510631, ChinaSchool of Mathematical Sciences, South China Normal University, Guangzhou 510631, ChinaWe consider a ratio-dependent predator-prey system with a mate-finding Allee effect on prey. The stability properties of the equilibria and a complete bifurcation analysis, including the existence of a saddle-node, a Hopf bifurcation, and, a Bogdanov-Takens bifurcations, have been proved theoretically and numerically. The blow-up method has been applied to investigate the structure of a neighborhood of the origin. Our mathematical results show the mate-finding Allee effect can reduce the complexity of system behaviors by making the complicated equilibrium less complicated, and it can be a destabilizing force as well, which makes the system has a high possibility of being threatened with extinction in ecology.http://dx.doi.org/10.1155/2014/673424 |
| spellingShingle | Ruiwen Wu Xiuxiang Liu Dynamics of a Predator-Prey System with a Mate-Finding Allee Effect Abstract and Applied Analysis |
| title | Dynamics of a Predator-Prey System with a Mate-Finding Allee Effect |
| title_full | Dynamics of a Predator-Prey System with a Mate-Finding Allee Effect |
| title_fullStr | Dynamics of a Predator-Prey System with a Mate-Finding Allee Effect |
| title_full_unstemmed | Dynamics of a Predator-Prey System with a Mate-Finding Allee Effect |
| title_short | Dynamics of a Predator-Prey System with a Mate-Finding Allee Effect |
| title_sort | dynamics of a predator prey system with a mate finding allee effect |
| url | http://dx.doi.org/10.1155/2014/673424 |
| work_keys_str_mv | AT ruiwenwu dynamicsofapredatorpreysystemwithamatefindingalleeeffect AT xiuxiangliu dynamicsofapredatorpreysystemwithamatefindingalleeeffect |