Bifurcation and control of a ratio-dependent bioeconomic model with time delay

In this paper, a singular delayed biological economic predator-prey system with ratio-dependent function is proposed. The conditions of singularity induced bifurcation and saddle-node bifurcation are gained and the existence of Hopf bifurcation are obtained by analyzing the distribution of roots of the corresponding characteristic equation, respectively. Further, a state feedback controller is designed to eliminate the singularity induced bifurcation and the hybrid control strategy is used to adjust the occurrence of Hopf bifurcation. Finally, numerical simulations are concluded to check the analytic results.