Nonlinear analysis and chaos control of the complex dynamics of multi-market Cournot game with bounded rationality

Abstract In this work, a dynamic multi-market Cournot model is introduced based on a multi-markets’ specific inverse demand function. Puu’s incomplete information approach, as a realistic method, is used to contract the corresponding dynamical model under this function. Therefore, some stability analysis is used by the model to detect the stability and instability conditions of the system’s Nash equilibrium. Based on the analysis, some dynamic phenomena such as bifurcation and chaos are found. Numerical simulations and the Maximum Lyapunov exponent are used to provide experimental evidence for the complicated behaviors of the system evolution. It is observed that the equilibrium points of the system can loose stability via flip bifurcation or Neimark–Sacher bifurcation and time-delayed feedback control is used to stabilize the chaotic behaviors of the system.

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