Dynamic Study For Two Factors Conflict Model With A Time Lag Effect

Conflict is a common social phenomenon in the social life, and its manifestations are varied. Such as marital conflict, culture, politics, ethnic conflict and the conflict between the national traditional war. Conflict can not only reduce the polarization of the two poles and the rigid of social system but also maintain the continuity of the society. This paper will study the two factors conflict model with time lag effect. The research of this model is of great significance both in theory and in real life.In this paper, we study the two factors conflict model with time lag effect. Firstly the research background and current situation of this model is introduced. Through numerical calculation, get the number of equilibrium points of the system; equilibrium point of the system is asymptotically stable sufficient conditions are obtained through the distribution of the roots of the characteristic equation. Secondly the model which has the conditional of Hopf branch is given, and through the center manifold theory and normal form method, the derived determine the explicit formula of bifurcating periodic solution stability and bifurcation direction. Finally, the numerical simulation to support the front analysis to this system dynamics, numerical simulation results and the theoretical line.