Dynamics of a Predator-Prey System Concerning Impulsive Effect

A mathematical model for dynamics of a prey dependent consumption model concerning impulsive control strategy is proposed and analyzed. By using Floquet theorem and comparison theorem of impulsive differential equation, we show that there exists a globally stable pest-eradication periodic solutions when the impulsive periodic is less than some critical values. Further, the conditions for the permanence of the system are given. We show the existence of nontrivial periodic solution if the pest eradication periodic solution losses its stability. When the unique positive periodic solution lose its stability, numerical simulations 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 periodic doubling bifurcation, symmetry breaking bifurcation, period halving bifurcation, quasi-periodic oscillation and chaos.