Dynamics study of nonlinear discrete predator-prey system with Michaelis-Menten type harvesting.

Abstract

In this paper, we study a discrete predator-prey system with Michaelis-Menten type harvesting. First, the equilibrium points number, local stability and boundedness of the system are discussed. Second, using the bifurcation theory and the center manifold theorem, the bifurcation conditions for the system to go through flip bifurcation and Neimark-Sacker bifurcation at the interior equilibrium point are obtained. A feedback control strategy is used to control chaos in the system, and an optimal harvesting strategy is introduced to obtain the optimal value of the harvesting coefficient. Finally, the numerical simulation not only shows the complex dynamic behavior, but also verifies the correctness of our theoretical analysis. In addition, the results show that the system causes nonlinear behaviors such as periodic orbits, invariant rings, chaotic attractors, and periodic windows by bifurcation.