Nonlinear dynamics and chaos control for a time delay Duffing system

International Journal of Nonlinear Sciences and Numerical Simulation

Volumn 6, Issue 2, 2005, Pages 187-199

  Ge, Zheng Ming ^a   Hsiao, Chun Lai ^a   Chen, Yen Sheng ^a  

^a NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

Bifurcation; Chaos; Dynamical system; Nonlinear dynamics; Stability

Indexed keywords

EID: 17844396932     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/IJNSNS.2005.6.2.187     Document Type: Article

References (21)

1. Lakshmanan, M. and Rajasekar, S., Nonlinear Dynamics, Springer-Verlag, New York, 2003
2. Thompson, J. M. T. and Stewart H. B., Nonlinear Dynamics and Chaos, Wiley, New York, 2002
3. Ge, Zheng-Ming and Leu, Wei-Ying, "Anti-Control of Chaos of Two-degrees-of-Freedom Louderspeaker System and Chaos Synchronization of Different Order Systems", Chaos, Solitons & Fractals Vol.20, pp.503-521, 2004
4. Ge, Zheng-Ming and Leu, Wei-Ying, "Chaos Synchronization and Parameter Identification for Loudspeaker System", Chaos, Solitons & Fractals Vol.21, pp.1231-1247, 2004
5. Ge, Zheng-Ming and Chen, Chien-Cheng, "Phase Synchronization of Coupled Chaotic Multiple Time Scales Systems", Chaos, Solitons & Fractals Vol.20, pp.639-647, 2004
6. Ge, Zheng-Ming and Chen, Yen-Sheng, "Synchronization of Unidirectional Coupled Chaotic Systems via Partial Stability", Chaos, Solitons & Fractals Vol.21, pp.101-111, 2004
7. Ge, Zheng-Ming, Cheng, Jui-Wen and Chen, Yen-Sheng, "Chaos Anticontrol and Synchronization of Three Time Scales Brushless DC Motor System", Chaos, Solitons & Fractals 22, pp.1165-1182, 2004
8. Ge, Zheng-Ming and Wu, Hong-Wen, "Chaos Synchronization and Chaos Anticontrol of a Suspended Track with Moving Loads", Journal of Sound and Vibration Vol.270, pp.685-712, 2004
9. Zhang, Y., Xu, J., "Classification and Computation of Non-resonant Double Hopf Bifurcations and Solutions in Delayed van der Pol-Duffing System", International Journal of Nonlinear Sciences and Numerical Simulation, 6(1), 2005, pp.63-68
10. Elabbasy, E. M., Agiza, H. N., El-Dessoky, M. M., "Controlling and Synchronization of Rossler System with Uncertain Parameters", International Journal of Nonlinear Sciences and Numerical Simulation, 5(2), pp. 171-182
11. Pyragas K., "Experimental Control of Chaos by Delayed Self-Controlling Feedback", Physical Letters A, Vol. 180, pp.99-102, 1993
12. Pyragas K., "Continuous Control of Chaos by Self-Controlling Feedback", Physical Letters A, Vol. 170, pp.421-428, 1992
13. Ge, Zheng-Ming, Developing Theory of Motion Stability, Gau Lih Book Company, Taipei, R.O.C, 2001
14. Razumikhin B. S., Stability of a System with one Time-Delay(R), PMM, 20, 4, pp. 500-512, 1956
15. Razumikhin B. S., Application of Lyapunov Method to the Stability of systems with Time-Delay(R), Automation and Telemechine, 21, 6, pp. 740-748, 1960
16. Qin, Y. X., Liu, Y. Q., Wang, L. and Zheng Z. X., Motion Stability of Dynamic Systems with Time Delay, Scientific Publisher, Beijing, 1989
17. Khailil, H. K, Nonlinear Systems, Prentice Hall, New Jersey, 2002
18. Poincaré, H., "Les Méthodes Nouvelles de la Mécanique Céleste", Gauthier-Villars, Paris, Vol. 3, 1899
19. Gollub, J. P. and Benson V. S., "Many Routes to Turbulent Convection", Journal of Fluid Mechanics, Vol. 100, pp. 449-470, 1980
20. Ianstiti, M., Hu, Q., Westervelt, R. M., and Tinkham, M., "Noise and Chaos in a Fractal Basin Boundary Regime in a Josephson Junction", Physical Review Letter, Vol. 55, pp. 746-749, 1985
21. Glimore, R. and Lefrance, M., The Topology of Chaos, Wiley, New York, 2002