We investigate a delayed stage-structured Ivlev’s functional response predator-prey model with impulsive stocking on prey and continuous harvesting on predator. Sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system are obtained. These results show that the behavior of impulsive stocking on prey plays an important role for the ...

w . m w . w . where f : 0, ` a 0, ` and the initial values x , . . . , x g 0, ` . 0 1ym Ž . In studying the global behavior of the solutions of Eq. 1 , we often need Ž . to establish that 1 is permanent, i.e., it has the property that every one of its solutions is eventually confined within a fixed compact interval regardless of the initial values chosen. Permanence is needed directly or indire...

The Lotka-Volterra competition model with diffusion and time delays has been the object of analysis by numerous authors under different approaches. For the case of two species, Ruan and Zhao 1 considered uniform persistence and global extinction; Lu 2 studied global attractivity, and Gourley and Ruan 3 analyzed stability and traveling fronts. The periodic case has also been considered, Feng and...