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Chin. Phys. B, 2011, Vol. 20(1): 010509    DOI: 10.1088/1674-1056/20/1/010509
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A new four-dimensional hyperchaotic Lorenz system and its adaptive control

Si Gang-Quan(司刚全), Cao Hui(曹晖), and Zhang Yan-Bin(张彦斌)
State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China
Abstract  Based on the Lorenz chaotic system, this paper constructs a new four-dimensional hyperchaotic Lorenz system, and studies the basic dynamic behaviours of the system. The Routh–Hurwitz theorem is applied to derive the stability conditions of the proposed system. Furthermore, based on Lyapunov stability theory, an adaptive controller is designed and the new four-dimensional hyperchaotic Lorenz system is controlled at equilibrium point. Numerical simulation results are presented to illustrate the effectiveness of this method.
Keywords:  hyperchaotic Lorenz system      adaptive control      Lyapunov stability theory  
Received:  10 June 2010      Revised:  09 August 2010      Accepted manuscript online: 
PACS:  05.45.Jn (High-dimensional chaos)  
  05.45.Gg (Control of chaos, applications of chaos)  
  05.45.Pq (Numerical simulations of chaotic systems)  

Cite this article: 

Si Gang-Quan(司刚全), Cao Hui(曹晖), and Zhang Yan-Bin(张彦斌) A new four-dimensional hyperchaotic Lorenz system and its adaptive control 2011 Chin. Phys. B 20 010509

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