On the dynamics of Kopel's Cournot duopoly model

In this paper we study the duopoly model proposed by M. Kopel [26], where two firms compete “a la Cournot” and the reaction curves have a higher degree of coupling in the sense that firms have to make their choices simultaneously. We will make a descriptive analysis of the two-dimensional model, making an approach through particular situations. On the other hand, when the firms are homogeneous a one-dimensional invariant subset is present in the model. We will give an analytical proof of the existence of a (topological) chaotic behavior for a wide range of parameter values and we will study when chaotic synchronization and collusion occur.