On the analysis of stability, bifurcation, chaos and chaos control of Kopel map (Q1125163)

The author deals with the Cournot duopoly problem, that is \[ \begin{aligned} x_{t+1} &= (1-\rho)x_t+ \rho\mu y_t(1- y_t),\\ y_{t+1} &= (1-\rho)y_t+ \rho\mu x_t(1-y_t) \end{aligned} \tag{1} \] where \(\rho,\mu\in \mathbb{R}_+\), \(x_t\) and \(y_t\) are production quantities. Here the author is interested only in positive solutions. He provides conditions for the stability of the fixed points and studies the bifurcation and chaos for (1), by computing the maximum Lyapunov exponents. Control of chaos is also discussed.