GLOBAL HOPF BIFURCATION OF A POPULATION MODEL WITH STAGE STRUCTURE AND STRONG ALLEE EFFECT

摘要

This paper is devoted to the study of a single-species population model with stage structure and strong Allee effect. By taking τ as a bifurcation parameter, we study the Hopf bifurcation and global existence of periodic solutions using Wu's theory on global Hopf bifurcation for FDEs and the Bendix-son criterion for higher dimensional ODEs proposed by Li and Muldowney. Some numerical simulations are presented to illustrate our analytic results using MATLAB and DDE-BIFTOOL. In addition, interesting phenomenon can be observed such as two kinds of bistability.