The dynamics of a prey-dependent consumption model concerning impulsive control strategy

A mathematical model for dynamics of a prey-dependent consumption model concerning impulsive control strategy is proposed and analyzed. We show that there exists a globally stable pest-eradication periodic solution when the impulsive period is less than some critical values. Further, the conditions for the permanence of system are given. We show the existence of nontrivial periodic solution if the pest-eradication periodic solution loses its stability. When the unique positive periodic solution lose its stability, numerical simulation shows there is a characteristic sequence of bifurcations, leading to a chaotic dynamics, which implies that the impulsive control model we considered has more complex dynamics including period-doubling bifurcation, symmetry-breaking bifurcation, period-halving bifurcation, quasi-periodic oscillation and chaos.