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Zbl 1232.92076
Wang, Jinfeng; Shi, Junping; Wei, Junjie
Predator-prey system with strong allee effect in prey. (English)
[J] J. Math. Biol. 62, No. 3, 291-331 (2011). ISSN 0303-6812; ISSN 1432-1416/e

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.

MSC 2000:: *92D40 Ecology
34C23 Bifurcation (periodic solutions)
34C05 Qualitative theory of some special solutions of ODE
34C60 Applications of qualitative theory of ODE
37N25 Dynamical systems in biology

Keywords: Global bifurcation; Limit cycles; Heteroclinic loop

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