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In this paper, a predator–prey model with double Allee effects and impulse is studied. The existence and stability of the prey-free periodic solution are investigated. The sufficient conditions for global… Click to show full abstract
In this paper, a predator–prey model with double Allee effects and impulse is studied. The existence and stability of the prey-free periodic solution are investigated. The sufficient conditions for global stability of the prey-free periodic solution are obtained. We also find a critical threshold that the predator and prey populations will coexist. The existence of the transcritical bifurcations is considered by means of the bifurcation theory when the prey population is not subject to Allee effect. Combining mathematical analysis and numerical simulations, we show that the double Allee effects and impulse greatly alter the outcome of the survival of both species.
Journal Title: Nonlinear Dynamics
Year Published: 2017
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