Predator-prey system with strong Allee effect in prey. (English) Zbl 1232.92076

Summary: Global bifurcation analysis of a class of general predator-prey models with strong Allee effect in the prey population is given in detail. We show the existence of a point-to-point heteroclinic orbit loop, consider Hopf bifurcations, and prove the existence/uniqueness and nonexistence of limit cycles for an appropriate range of parameters. For a unique parameter value, a threshold curve separates the overexploitation and coexistence (successful invasion of predators) regions of initial conditions. Our rigorous results justify some recent ecological observations, and practical ecological examples are used to demonstrate our theoretical work.


92D40 Ecology
34C23 Bifurcation theory for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
37N25 Dynamical systems in biology


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