Chaotic Analysis of a Cournot Model with the Behavior Rule of Short-Sighted Eyes

In this paper, a nonlinear dynamical system is established for a Cournot duopoly model with the behavior rule of short-sighted eyes. The equilibrium points and their local stability are investigated. This model exhibits some chaotic behaviors in a certain range of the output adjusted coefficients. It is proved that the system is chaotic in the sense of both Devaney and Li-Yorke by employing the snap-back repeller theory. The complicated dynamical behaviors of the model are observed by computer simulations. In particular, this model exhibits a strange attractors when the output adjusted coefficients are taken as some different values.