Hopf bifurcation and nonlinear state feedback control for a modified Lotka-Volterra differential algebraic predator-prey system

Abstract

This paper systematically studies a modified Lotka-Volterra differential algebraic predator-prey system, which is combined with nonlinear harvesting in prey and gestation delayed for predator. According to the stability and bifurcation theorem, through considering gestation delayed as a bifurcation parameter, the occurrence of Hopf bifurcation of proposed system is shown. Moreover, the nonlinear state feedback controller is designed to control the Hopf bifurcation, and the population of prey and predator can be driven to steady states by adjusting harvesting costs and the economic profit. Lastly, numerical simulations illustrate the effectiveness of the results obtained here.