The dynamics of an eco-epidemic model with distributed time delay and impulsive control strategy

In this paper, we investigate an eco-epidemic model with distributed time delay and impulsive control strategy. Firstly, by using Floquet theory of impulsive differential equation, we get the condition for the local stability of the prey eradication periodic solutions. Secondly, by means of impulsive equation compare theory, we get the condition for the global asymptotical stability of the prey eradication periodic solutions. Finally we study the permanence of the system. Numerical simulations (bifurcation diagram, the largest Lyapunov exponents and power spectra) are carried out to illustrate the above theoretical analysis and the rich dynamics phenomenon, which are caused by impulsive effects and time delay, for example bifurcation, double period solution, etc.