Dynamics of a predator-prey ecological system with nonlinear harvesting rate

Abstract

In this paper, a predator-prey ecological economic system with nonlinear harvesting rate is formulated and studied. This system is described by a differential-algebraic equation. By employing local parameterization method, an equivalent differential system with parameter is obtained. Then by normal form theory and bifurcation theory, the complex dynamics of the system are investigated, including the local stability of equilibrium point and Hopf bifurcation. Finally, MATLAB simulation illustrates the effectiveness of our results.