Chaos control of Chen chaotic dynamical system. (English) Zbl 1038.37029

Summary: This paper is devoted to study the problem of controlling chaos in a Chen chaotic dynamical system. Two different methods of control, feedback and nonfeedback methods are used to suppress chaos to unstable equilibria or unstable periodic orbits (UPO). The Lyapunov direct method and Routh-Hurwitz criteria are used to study the conditions of the asymptotic stability of the steady states of the controlled system. Numerical simulations are presented to show these results.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93C10 Nonlinear systems in control theory
37N35 Dynamical systems in control
Full Text: DOI


[1] Ott, E.; Grebogi, C.; Yorke, J.A., Controlling chaos, Phys. rev. lett., 64, 1179-1184, (1999)
[2] Ahmed, E.; Agiza, H.N.; Hassan, S.Z., On modelling advertisement in Cournot duopoly, Chaos, solitons & fractals, 10, 7, 1179-1184, (1999) · Zbl 0957.91066
[3] Agiza, H.N., On the analysis of stability, bifurcation, chaos and chaos control of kopel map, Chaos, solitons & fractals, 10, 11, 1909-1916, (1999) · Zbl 0955.37022
[4] Chen, G., On some controllability conditions for chaotic dynamics control, Chaos, solitons & fractals, 8, 9, 1461-1470, (1997)
[5] Ahmed, E.; Elmisiry, A.; Agiza, H.N., On controlling chaos in an inflation-unemployment dynamical system, Chaos, solitons & fractals, 10, 9, 1567-1570, (1999) · Zbl 0958.91042
[6] Pyragas, K., Continuous control of chaos by self-controlling feedback, Phys. lett. A, 170, 421-428, (1992)
[7] Hegazi, A.; Agiza, H.N.; El-Dessoky, M.M., Controlling chaotic behaviour for spin generator and roessler dynamical systems with feedback control, Chaos, solitons & fractals, 12, 631-658, (2001) · Zbl 1016.37050
[8] Ramirez, J., Nonlinear feedback for control of chaos from a piecewise linear hysteresis circuit, IEEE trans. circuits syst., 42, 168-172, (1995)
[9] Hwang, C.; Hsheh, J.; Lin, R., A linear continuous feedback control of Chua’s circuit, Chaos, solitons & fractals, 8, 9, 1507-1515, (1997)
[10] Rajasekar, S.; Murreali, K.; Lakshmanan, M., Control of chaos by nonfeedback methods in a simple electronic circuit system and the fitz hugh – nagumo equation, Chaos, solitons & fractals, 8, 9, 1554-1558, (1997)
[11] Hwang, C.; Chow, H.; Wang, Y., A new feedback control of a modified Chua’s circuit system, Physica D, 92, 95-100, (1996) · Zbl 0925.93366
[12] Hwang, C.; Hsieh, J., A linear continuous feedback control of Chua’s, Chaos, solitons & fractals, 8, 9, (1997)
[13] Chen, G.; Ueta, T., Yet another chaotic attractor, Internat. J. bifurcation chaos, 9, 7, 1465-1466, (1999) · Zbl 0962.37013
[14] Keshet, L.E., Mathematical models in biology, (1988), Random House New York · Zbl 0674.92001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.