State Feedback Impulsive Control of a Prey-Predator System with Constant Release of Prey Population in Toxin Environment

Abstract

River crab is a freshwater breeding species with higher economic value, and the river crab breeding industry has developed rapidly in recent years. As the river crab is at the top of the food chain in the lake, the increasingly serious water pollution has a great impact on the growth and reproduction of the river crab population. A model is established to describe the growth and state feedback impulsive harvest of river crab in toxin environment, and the existence, uniqueness and stability of the first-order periodic solution of the state feedback impulsive system are studied. The numerical simulation at the end of this paper verifies the correctness of the theory, and the conclusion provides a theoretical support for improving the economic benefits of river crab culture.