On stability and bifurcation of Chen's system

Chaos, Solitons and Fractals

Volumn 19, Issue 5, 2004, Pages 1269-1282

  Li, TieCheng ^a   Chen, Guanrong ^b   Tang, Yun ^a  

^a TSINGHUA UNIVERSITY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; COMPUTATIONAL METHODS; CONTROL SYSTEM ANALYSIS; FEEDBACK CONTROL;

QUADRATIC SYSTEMS;

SYSTEM STABILITY;

EID: 0141839040     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(03)00334-5     Document Type: Article

References (28)

1. Agiza H.N., Yassen M.T. Synchronization of Rössler and Chen chaotic dynamical systems using active control. Phys. Lett. A. 278:2001;191-197.
2. Celikovský S., Chen G. On a generalized Lorenz canonical form of chaotic systems. Int. J. Bifurcat. Chaos. 12:2002;1789-1812.
3. Chen G. Controlling chaos and bifurcations in engineering systems. 1999;CRC Press, Boca Raton.
4. Chen G. Chaotification via feedback: the discrete case. Chen G., Yu X. Chaos control: theory and applications. 2003;159-178 Springer-Verlag, Heidelburg.
5. Chen G., Dong X. From chaos to order: methodologies. perspectives and applications. 1998;World Scientific, Singapore.
6. Chen G., Lai D. Anticontrol of chaos via feedback. Int. J. Bifurcat. Chaos. 8:1998;1585-1590.
7. Chen S.H., Lü J. Synchronization of an uncertain unified chaotic system via adaptive control. Chaos, Solitons & Fractals. 14:2002;643-647.
8. Guan X.P., Fan Z.P., Peng H.P., Wang Y.Q. The adaptive control of Chen's chaotic systems. Acta Phys. Sinica. 50:2001;2108-2111.
9. Guan Z.H., Liao R.Q., Zhou F., Wang H.O. On impulsive control and its application to Chen's chaotic systems. Int. J. Bifurcat. Chaos. 12:2002;1191-1197.
10. Kuznetsov Y.A. Elements of applied bifurcation theory. 1995;Springer-Verlag, New York.
11. Li C., Chen G. A note on Hopf bifurcation in Chen's system. Int J Bifurcat Chaos. 13:2003;1609-1615.
12. Li Z, Han C, Han J. Robust adaptive control of Rössler and Chen chaotic systems. In: Proc NOLTA 2002, Xi'an, China, 7-11 October 2002, p. 223-6.
13. Lu J.A., Lü J., Chen S.H. Chen's chaotic attractor and its characteristic quantity. Contr. Theory Appl. 19:2002;308-310.
14. Lü J., Chen G., Cheng D., Celikovský S. Bridge the gap between the Lorenz system and the Chen system. Int. J. Bifurcat. Chaos. 12:2002;2917-2926.
15. Lü J., Chen G., Zhang S. Controlling in between the Lorenz and the Chen systems. Int. J. Bifurcat. Chaos. 12:2002;1417-1422.
16. Lü J., Zhang S. Controlling Chen's chaotic attractor using backstepping design based on parameters identification. Phys. Lett. A. 286:2001;148-152.
17. Lü J., Zhou T., Chen G., Zhang S. Local bifurcation of the Chen system. Int. J. Bifurcat. Chaos. 12:2002;2257-2270.
18. Lü J., Zhou T., Zhang S. Chaos synchronization between linearly coupled chaotic systems. Chaos, Solitons & Fractals. 14:2002;529-541.
19. Lü J., Zhou T., Zhang S. Controlling Chen's chaotic attractor using feedback function based on parameters identification. Chinese Phys. 11:2002;12-16.
20. Luo D.et al. Bifurcation theory and methods of dynamical systems. 1997;World Scientific, Singapore.
21. Ueta T., Chen G. Bifurcation analysis of Chen's attractor. Int. J. Bifurcat. Chaos. 10:2002;1917-1931.
22. Wang X. Chen's attractor - A new chaotic attractor. Contr. Theory Appl. 16:2000;779.
23. Wang X., Chen G. Chaotification via arbitrarily small feedback controls. Int. J. Bifurcat. Chaos. 10:2000;549-570.
24. Wang X., Chen G., Yu X. Anticontrol of chaos in continuous-time systems via time-delayed feedback. Chaos. 10:2000;771-779.
25. Yang B.L., Yang T. Sampled data feedback control of Chen's system. Acta Phys. Sinica. 49:2000;1039-1042.
26. Yassen M.T. Chaos control of Chen chaotic dynamical system. Chaos, Solitons & Fractals. 15:2003;271-283.
27. Yu X., Xia Y. Detecting unstable periodic orbits in Chen's chaotic attractor. Int. J. Bifurcat. Chaos. 10:2001;1987-1991.
28. Zhong G.Q., Tang K.S. Circuitry implementation and synchronization of Chen's attractor. Int. J. Bifurcat. Chaos. 12:2002;1423-1427.