The Research Of Chaotic Dynamics And Chaos Control Of A Nonlinear Duopoly Stackelberg Game

In oligopoly markets,every enterprise has a significant impact on price and outputs of the products.Enterprises need to consider competitors' response and consumers' choice into decision-making process.The uncertainty of strategies brings about many models for describing the enterprise decision-making behavior,such as Stackelberg game,a dynamic model of oligopoly market.Stackelberg game is consistent with many realistic situation and explains the characteristics of enterprise decision-making behavior well.Basing on previous works,we assume that the cost function is nonlinear,and two enterprises involved adopt different expectation types.One is bounded rational expectation and another is adaptive expectation.The method of dynamic equilibrium solution is obtained by reverse Nash induction and the dynamic Stackelberg duopoly quantity competition model is put forward.The stability region is analyzed by using the theory of stability.Furthermore,some other behaviors of Stackelberg game are studied,such as,fractal dimension,bifurcation,chaos and chaos control.Then a Stackeberg game with delayed strategies is formulated which is more in line with reality.Numerical simulations demonstrate that the parameter adaptive feedback control method can force the chaos back to stability effectively,and appropriate delay coefficient could enlarge the stability domain.