Estimating the bound for the generalized Lorenz system

doi:10.1088/1674-1056/19/1/010505

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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