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Chin. Phys. B, 2010, Vol. 19(1): 010505    DOI: 10.1088/1674-1056/19/1/010505
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Estimating the bound for the generalized Lorenz system

Zheng Yu, Zhang Xiao-Dan
Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, China
Abstract  A chaotic system is bounded, and its trajectory is confined to a certain region which is called the chaotic attractor. No matter how unstable the interior of the system is, the trajectory never exceeds the chaotic attractor. In the present paper, the sphere bound of the generalized Lorenz system is given, based on the Lyapunov function and the Lagrange multiplier method. Furthermore, we show the actual parameters and perform numerical simulations.
Keywords:  chaos      generalized Lorenz system      Lyapunov function      Lagrange multiplier method  
Received:  10 October 2008      Revised:  15 July 2009      Published:  15 January 2010
PACS:  05.45.Pq (Numerical simulations of chaotic systems)  
  02.60.Lj (Ordinary and partial differential equations; boundary value problems)  
  05.45.Gg (Control of chaos, applications of chaos)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60674059), and Research Fund of University of Science and Technology Beijing, China (Grant No. 00009010).

Cite this article: 

Zheng Yu, Zhang Xiao-Dan Estimating the bound for the generalized Lorenz system 2010 Chin. Phys. B 19 010505

[1] Lorenz E N 1963 J. Atoms. Sci. 20 130
[2] Chen G R and Ueta T 1999 Int. J. Bifurc. Chaos 9 1465
[3] Lü J H and Chen G R 2002 Int. J. Bifurc. Chaos 12 659
[4] Van\v e\v cek A and \v Celikovsk\v y S 1996 Control Systems: from Linear Analysis to Synthesis of Chaos (London: Prentice-Hall)
[5] Chen G R and Lü J H 2001 The Lorenz Family System Dynamics Analysis, Control and Synchronization (Beijing: Science Press) p151
[6] Cai N, Jing Y W and Zhang S Y 2009 Acta Phys. Sin. 58 802 (in Chinese)
[7] Zhang X D and Zhang L L 2006 Commun. Theor. Phys. 45 461
[8] Niu Y D, Ma W Q and Wang Y 2009 Acta Phys. Sin. 58 2934 (in Chinese)
[9] Zhang X D, Zhang L L and Min L Q 2003 Chin. Phys. Lett. 20 2114
[10] W D Q and Luo X S 2008 Chin. Phys. B 17 92
[11] Yan S L 2007 Chin. Phys. 16 3271
[12] Wang S, Cai L, Li Q and Wu G 2007 Chin. Phys. 16 2631
[13] Leonov G, Bunin A and Koksch N 1987 ZAMM 67 649
[14] Zhou T, Tang Y and Chen G R 2003 Int. J. Bifurc. Chaos 13 2561
[15] Li D M, Lu J A, Wu X Q and Chen G R 2005 Chaos, Solitons and Fractals 23 529
[16] Li D M, Lu J A, Wu X Q and Chen G R 2006 J. Math. Appl. 323 844
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