Bifurcation analysis and control for a class of predator-prey system with harvesting

Abstract

A harvested predator-prey system with Holling type II functional response and a constant prey refuge is proposed. Compared with other researches on dynamics of predator-prey population, this system is described by differential-algebraic equations due to economic factor. By choosing m as bifurcation parameter and using the new normal form of differential-algebraic systems, center mainfold theorem and bifurcation theory, we get the stability and the Hopf bifurcation of the proposed system. We believe the new effective analytical method here enriches the toolbox for the qualitative analysis of the differential-algebraic systems. Finally, numerical simulations illustrate the effectiveness of our results.