Application Of The Prey-predator System In Biological Resource Management

First, we introduce the research summary of prey-predator model and some of the relevant knowledge, and then give the major works in this paper.Next, we propose and investigate a predator-prey system with time delay and stage structure for the predator. By using the stability theory of differential equation, we discuss the positive and bounded of the solutions, and discuss the existence and stability of the equilibria. By using persistence theory on infinite dimensional systems, we discuss the uniform permanence of the system. Sufficient conditions are obtained for the permanence of the system and the global stability of the equilibria. Numerical simulations are carried out to illustrate the main results.Then, according to the reality of biological resource management, we propose and study a delayed and stage-structured predator-prey model with impulsive stocking prey and continuous harvesting predator. Using the theories and methods of impulsive delayed differential equations, we discuss the positive and bounded of the solutions, the existence and the global attractivity of the predator-extinction periodic solution and the uniform permanence of the system. Sufficient conditions for the global appeal of predator-extinction of periodic solutions and the permanence of the system are obtained. Numerical simulations are carried out to illustrate the main results.Finally, we give the study problems and direction in the biological resource management.