Bifurcation analysis for a ratio-dependent predator-prey system with multiple delays

Abstract

In this paper, we consider a ratio-dependent predator-prey system with multiple delays where the dynamics are logistic with the carrying capacity proportional to prey population. By choosing the sum τ of two delays as the bifurcation parameter, the stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.

Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system

“…In this modified model, predator density is logistic with time delay and the carrying capacity proportional to prey density. In [29], Lv et al considered a ratio-dependent predator-prey model with multiple delays where the dynamics are logistic with the carrying capacity proportional to prey population. They investigated the stability of the positive fixed point and the presence of Hopf bifurcation.…”