Bogdanov-takens bifurcation for a predator-prey system with holling type IV function

摘要

This paper considers the dynamics of a delayed predator-prey system with generalized Holling type IV functional response. The conditions are presented under which the unique positive equilibrium of this system is a Bogdanov-Takens (B-T) singularity. By using the normal form theory and the center manifold reduction theorem, the normal form is obtained for the B-T singularity. Finally, numerical simulations are given to illustrate the theoretical results derived.