Hopf bifurcation for a differential–algebraic biological economic system with time delay

In this paper, we consider a differential–algebraic biological economic system with time delay and harvesting where the dynamics is logistic with the carrying capacity proportional to prey population. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the differential–algebraic biological economic system based on the normal form approach and the center manifold theory. At last, numerical simulations are performed to illustrate the analytical results.