Abstract
The paper is devoted to exploring the complex dynamics of a Cournot–Bertrand model, where one agent chooses quantity and the other chooses price. A nonlinear discrete system is built to illustrate the game model with bounded rationality. Theoretically, the local and global stability of equilibrium are investigated. The simulation reveals that Flip and Neimark–Sacker bifurcation phenomena occur when the adjustment speed of one firm increases through different boundary curves. Therefore three different chaotic attractors are presented. The standard Logistic mapping is applied to analyze the dynamics of the system on invariant axes. The critical curves classify the number of preimage of the quantity or price. Besides, simulations give more intuitive results: the cycle attractor, chaotic attractor and the basin of attraction with “holes” are given.
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