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A Holling type III functional response predator-prey system with constant gestation time delay and impulsive perturbation on the prey is investigated. The sufficient conditions for the global attractivity of a predator-extinction periodic solution are obtained by the theory of impulsive differential equations, i.e. the impulsive period is less than the critical value T1∗$T_{1}^{*}$. The conditions for the permanence of the system are investigated, i.e. the impulsive period is larger than the critical value T2∗$T_{2}^{*}$. Numerical examples show that the system has very complex dynamic behaviors, including (1) high-order periodic and quasi-periodic oscillations, (2) period-doubling and -halving bifurcations, and (3) chaos and attractor crises. Further, the importance of the impulsive period, the gestation time delay, and the impulsive perturbation proportionality constant are discussed. Finally, the impulsive control strategy and the biological implications of the results are discussed.

A delayed Holling type III functional response predator-prey system with impulsive perturbation on the prey