Dynamic analysis of a kind of species control model concerning impulsively releasing pathogen and infective predator

A kind of species control model concerning impulsive releasing pathogen and infective predator is presented. By using the Floquet theory and comparison theorem of impulsive differential equation, the extinction and permanence of system are discussed and the corresponding conditions are obtained, respectively. Finally, the practical meanings of those conditions are explained and the theoretical results are confirmed by numerical simulations. Besides, with the period of impulsive release varying, the numerical simulations also show that the system displays a series of complex phenomena which include period-doubling cascade, chaos and periodic window, etc.