Hopf bifurcation for a predator–prey biological economic system with Holling type II functional response

In this paper, a biological economic system which considers a prey–predator system with Holling type II functional response and harvest effort on prey is proposed. By using the differential-algebraic system theory and Hopf bifurcation theory, Hopf bifurcation of the proposed system is investigated. Different from previous researches on the dynamic behaviors of predator–prey systems, our model is described by differential-algebraic equations due to the economic factor. The economic profit is chosen as a positive bifurcation parameter here. It is found that a phenomenon of Hopf bifurcation occurs as the economic profit increases beyond a certain threshold. Lastly, with the help of Matlab software, numerical simulations are carried out to demonstrate the effectiveness of our results.