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

Ruiwen Wu and Xiuxiang Liu

Abstract and Applied Analysis, 2014, vol. 2014, 1-14

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
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:673424

DOI: 10.1155/2014/673424

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