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.