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Wu, Ruiwen; Liu, Xiuxiang

Dynamics of a predator-prey system with a mate-finding Allee effect. (English) Zbl 1474.92088

Abstr. Appl. Anal. 2014, Article ID 673424, 14 p. (2014).
Summary: 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.

MSC:

92D25 Population dynamics (general)
37N25 Dynamical systems in biology
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