Qualitative Analysis of a Class of Multimolecules Saturated Reaction Dynamical System

A class of multimolecules saturated reaction model was studied and the stability of equilibrium was discussed.The limit cycle and the Hopf bifurcation behavior of the system were studied.The conditions of existence and uniqueness of limit cycles were obtained by using the qualitative theory of ordinary differential equations.The Hopf bifurcation behavior of the dynamic system was exploited by using the method of normal form theory and other approaches.It shows that the first order weak focus is stable.When the positive singular point is unstable,the system has unique stable limit cycle in the neighborhood of this critical point.At last we compared qualitative property of different systems with saturated reaction speed.