Dynamics of a Predator‐Prey System with a Mate‐Finding Allee Effect

Ruiwen Wu and Xiuxiang Liu

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: 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.

Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2014/673424

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:673424

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().