The Complexity of a Repeated Bertrand Model with Multi Parameters

We establish a nonlinear dynamical Bertrand model in this paper to study the oligopolistic competition strategy. The price adjustment parameter and the weight factors of profit and market share are introduced into the model to present the competitors´ decision with bounded rationality. We study the complexity of the model via using the theory of bifurcations of dynamical systems. The results of numerical simulation show that both parameters might change the system stability at the Nash equilibrium point and cause bifurcation and chaos. The state feedback and parameter adjustment method is applied to control the chaos.