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Complex Dynamics and Chaos Control in nonlinear Four-Oligopolist Game with Different Expectations

A dynamic four-oligopolist game characterized by firms with different expectations is modeled by four-dimensional nonlinear difference equations, where the market has a quadratic inverse demand function and the firm possesses a cubic total cost function. The Nash equilibrium of the local stability of the proposed model is studied. Then the bifurcation diagrams and Lyapunov exponents of the system are presented to show that four-oligopolist game model behaves chaotically with the variation of the parameters. Finally, the state variables' feedback and parameter variation method are effectively used to control the delay in the appearance of bifurcation.