1. Dynamics of a predator-prey system with a mate-finding Allee effect on prey
- Author
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Xiuxaing Liu and Ruiwen Wu
- Subjects
Mathematics::Dynamical Systems ,Ecology ,General Mathematics ,Dynamics (mechanics) ,Predator-prey system,mate-finding Allee effect,nonmonotonic functional response,Bogdanov-Takens bifurcation,heteroclinic curve,homoclinic loop ,Predation ,symbols.namesake ,symbols ,Quantitative Biology::Populations and Evolution ,Bogdanov–Takens bifurcation ,Nonlinear Sciences::Pattern Formation and Solitons ,Mathematical economics ,Mathematics ,Allee effect - Abstract
We consider a predator--prey system with nonmonotonic functional response and a hyperbolic type of mate-finding Allee effect on prey. A detailed mathematical analysis of the system, including the stability and a series of bifurcations (a saddle-node, a Hopf, and a Bogdanov--Takens bifurcation), has been given. The mathematical results show that the system is highly sensitive to the parameters and initial status. It exhibits a stable limit cycle, or different types of heteroclinic curves, or a homoclinic loop when parameters take suitable values.
- Published
- 2017
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