Open Access
2014 Dynamics of a Predator-Prey System with a Mate-Finding Allee Effect
Ruiwen Wu, Xiuxiang Liu
Abstr. Appl. Anal. 2014: 1-14 (2014). DOI: 10.1155/2014/673424


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.


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Ruiwen Wu. Xiuxiang Liu. "Dynamics of a Predator-Prey System with a Mate-Finding Allee Effect." Abstr. Appl. Anal. 2014 1 - 14, 2014.


Published: 2014
First available in Project Euclid: 27 February 2015

zbMATH: 07022852
MathSciNet: MR3273913
Digital Object Identifier: 10.1155/2014/673424

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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