Analysis of a Predator-Prey System Concerning Impulsive Effect

Abstract

A stage-structured predator-prey model with impulses is proposed and investigated. According to the fact of biological resource management, it is assumed that the immature individuals and the mature individuals of the predator population are divided by fixed age and that immature predator population does not have the ability to attack prey. Sufficient conditions, which guarantee the global attractivity of predator-extinction periodic solution and the permanence of the system, are obtained. Furthermore, numerical simulations shows there is a characteristic sequence of bifurcations, leading to a chaotic dynamics, which implies that the impulsive control model we considered has more complex dynamics including periodic doubling bifurcation, symmetry breaking bifurcation, period halving bifurcation, quasi-periodic oscillation and choas.