On the Analysis of Stability, Bifurcation, Chaos and Chaos Control of Kopel Map

A dynamical system of two nonlinear difference equations introduced by Kopel is studied (Kopel, M., Simple and complex adjustment dynamics in Cournot Duopoly model, Chaos, Solitons and Fractals, 1996, 7 (12), 2031–2048.). In this study, we determine conditions for the stability of the fixed points and we study the bifurcations and chaos (Devany, R. L., Introduction to Chaotic Dynamical Systems. Addison–Wesley, New York, 1989.) by computing the maximum Laypunov exponents (Luhta, I. and Virtanen, I., Chaos, Solitons and Fractals, 1996, 7, 2083.). The OGY chaos control formula is used to control chaos in this system.