Impulsive Control Of A Prey System With Functional Reaction Function

Impulsive differential equation presents the quick change or jump of some states of motion at the fixed or varied time. It reflects the developing process of nature more actually. Impulsive control of biological population becomes an interesting and challenging research task in the fields of biological control. Impulsive differential equation has shown all-right applicative prospect in the study of population dynamics.In this paper we principally study that impulsive differential equation theory applies to predator-prey ecosystem with functional reaction function x^1/2 . The notions of the trivial solution's stability for the linear impulsive differential system are defined. Then the sufficient conditions for the solution's stability of nonlinear impulsive differential system are given by applying the relations of the parameter's variation and comparison principle. After that based on the complexity of population ecosystem, the models are modified. Next we investigate the stable problem of both a predator-prey ecosystem with functional reaction function x^1/2 respectively. Then we get the sufficient condition for this system's unstable positive equilibrium to asymptotic stability in the proper condition by the impulsive control. And densities of predator and prey individually exist around a constant. Further more, the paper gives ecological explanation. Thereafter, based on three-species system with functional reaction function, the function is specified as x^1/2. Then we study a predator-prey ecosystem with functional reaction function x^1/2 by using the linear approximate method of impulsive control system. The sufficient condition for this system's unstable positive equilibrium to asymptotic stability by the impulsive control is obtained in the discussion. And the species arrive at a new stable state in which they can coexist and development. Finally, the paper gives ecological explanation by figure simulation.