Qualitative Analysis Of A SIRS Model

This article applies the method of bifurcation theory of dynamical system, it studies the Hopf bifurcation and the homoclinic bifurcation of a SIRS model, proving the existence of the Hopf bifurcation, moreover, it calculates the parameter condition of deciding the direction and stability of the Hopf bifurcation. The last, it shows the condition of the limit-cycle appearing in the homoclinic loop bifurcation and the uniqueness of the limit-cycle.