Predator-prey system with strong Allee effect in prey.
Global bifurcation analysis of a class of general predator-prey models with a strong Allee effect in prey population is given in details. We show the existence of a point-to-point heteroclinic orbit loop, consider the Hopf bifurcation, and prove the existence/uniqueness and the nonexistence of limit cycle for appropriate range of parameters. For a unique parameter value, a threshold curve separates the overexploitation and coexistence (successful invasion of predator) regions of initial conditions. Our rigorous results justify some recent ecological observations, and practical ecological examples are used to demonstrate our theoretical work.
Wang
Jinfeng
J
Department of Mathematics, Harbin Institute of Technology, Heilongjiang, People's Republic of China. jfwang_math@sohu.com
Shi
Junping
J
Wei
Junjie
J
D000818:Animals; D017753:Ecosystem; D020387:Food Chain; D055641:Mathematical Concepts; D008954:Models, Biological; D011157:Population Dynamics; D011235:Predatory Behavior