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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(郑宇) and Zhang Xiao-Dan(张晓丹)
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      Accepted manuscript online: 
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(郑宇) and Zhang Xiao-Dan(张晓丹) Estimating the bound for the generalized Lorenz system 2010 Chin. Phys. B 19 010505

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