Dynamical Behavior for a Food-Chain Model with Impulsive Harvest and Digest Delay

Abstract

We investigate the dynamics of a food-chain system with digest delay and periodic harvesting for the prey. By using the comparison theorem, small amplitude skills in the impulsive differential equation, and a special qualitative analysis method in the delay differential equation, we prove that there exists a predators-eradication periodic solution which is globally attractive and show that the pest population can be controlled under the economic threshold level and the system can be uniformly permanent when the harvest period $T$ is long enough or the harvesting rate $\delta$ is not too large. Furthermore, we perform a series of numerical simulations to display the effects of the digest delay and periodic harvesting on the dynamic behavior of the food-chain system.