论文信息 - On the Analysis of Stability, Bifurcation, Chaos and Chaos Control of Kopel Map

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

Abstract 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.

H. N. Agiza | H. Agiza

[1] Elsayed Ahmed,et al. On Modelling Advertisement in Cournot Duopoly , 1999 .

[2] Ying-Cheng Lai,et al. Controlling chaos , 1994 .

[3] Michael Kopel,et al. Simple and complex adjustment dynamics in Cournot duopoly models , 1996 .

[4] Leo Kaas,et al. Stabilizing chaos in a dynamic macroeconomic model , 1998 .

[5] R. Devaney. An Introduction to Chaotic Dynamical Systems , 1990 .

[6] M. Sonis. Once more on Hénon map: Analysis of bifurcations , 1996 .

[7] Ilkka Virtanen,et al. Non-linear advertising capital model with time delayed feedback between advertising and stock of goodwill , 1996 .