A new four-dimensional hyperchaotic Lorenz system and its adaptive control

doi:10.1088/1674-1056/20/1/010509

中国物理B ›› 2011, Vol. 20 ›› Issue (1): 10509-010509.doi: 10.1088/1674-1056/20/1/010509

A new four-dimensional hyperchaotic Lorenz system and its adaptive control

司刚全, 曹晖, 张彦斌

State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China

收稿日期:2010-06-10 修回日期:2010-08-09 出版日期:2011-01-15 发布日期:2011-01-15

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

Received:2010-06-10 Revised:2010-08-09 Online:2011-01-15 Published:2011-01-15

摘要/Abstract

摘要： 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.

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.

Key words: hyperchaotic Lorenz system, adaptive control, Lyapunov stability theory

中图分类号: (High-dimensional chaos)

05.45.Jn

05.45.Gg (Control of chaos, applications of chaos) 05.45.Pq (Numerical simulations of chaotic systems)

司刚全, 曹晖, 张彦斌. A new four-dimensional hyperchaotic Lorenz system and its adaptive control[J]. 中国物理B, 2011, 20(1): 10509-010509.

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[J]. Chin. Phys. B, 2011, 20(1): 10509-010509.

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A new four-dimensional hyperchaotic Lorenz system and its adaptive control

A new four-dimensional hyperchaotic Lorenz system and its adaptive control

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