Species Permanence Analysis of an Ecological Model with an Impulsive Control Strategy

Abstract:

      In this paper, on the basis of the theories and methods of ecology and ordinary differential equations, an ecological model with an impulsive control strategy is established. By using the theories of impulsive equations, small amplitude perturbation skills and comparison technique, we get the condition which guarantees the global asymptotical stability of the prey-$x$-eradication and predator-$y$-eradication periodic solution. It is proved that the system is permanent. Furthermore, numerical simulations are also illustrated which agree well with our theoretical analysis. All these results may be useful in study of the dynamic complexity of ecosystems.