Hopf bifurcation in a delayed differential–algebraic biological economic system

In this paper, we consider a differential–algebraic biological economic system with time delay where the model with Holling type II functional response incorporates a constant prey refuge and prey harvesting. By considering time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the differential–algebraic biological economic system based on the new normal form approach of the differential–algebraic system and the normal form approach and the center manifold theory. Finally, numerical simulations illustrate the effectiveness of our results.