A novel one equilibrium hyper-chaotic system  generated upon Lü attractor

doi:10.1088/1674-1056/19/2/020507

中国物理B ›› 2010, Vol. 19 ›› Issue (2): 20507-020507.doi: 10.1088/1674-1056/19/2/020507

A novel one equilibrium hyper-chaotic system generated upon Lü attractor

陈增强¹, 袁著祉¹, 贾红艳²

(1)Department of Automation, Nankai University, Tianjin 300071, China; (2)Department of Automation, Nankai University, Tianjin 300071, China;Department of Automation, Tianjin University of Science and Technology, Tianjin 300222, China

收稿日期:2009-02-27 修回日期:2009-05-31 出版日期:2010-02-15 发布日期:2010-02-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 60774088 and 10772135), the Research Foundation from the Ministry of Education of China (Grant No. 107024) and the Program for New Century Excellent Talents in University of China (NCET), and the Application Base and Frontier Technology Project of Tianjin, China (Grant No. 08JCZDJC21900), and the Scientific Research Foundation for the Returned Overseas Scholars of the State Education Ministry.

A novel one equilibrium hyper-chaotic system generated upon Lü attractor

Jia Hong-Yan(贾红艳)^a)b)^†, Chen Zeng-Qiang(陈增强)^a)^‡, and Yuan Zhu-Zhi(袁著祉)^a)

^a Department of Automation, Nankai University, Tianjin 300071, China; ^b Department of Automation, Tianjin University of Science and Technology, Tianjin 300222, China

Received:2009-02-27 Revised:2009-05-31 Online:2010-02-15 Published:2010-02-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 60774088 and 10772135), the Research Foundation from the Ministry of Education of China (Grant No. 107024) and the Program for New Century Excellent Talents in University of China (NCET), and the Application Base and Frontier Technology Project of Tianjin, China (Grant No. 08JCZDJC21900), and the Scientific Research Foundation for the Returned Overseas Scholars of the State Education Ministry.

摘要/Abstract

摘要： By introducing an additional state feedback into a three-dimensional autonomous chaotic attractor Lü system, this paper presents a novel four-dimensional continuous autonomous hyper-chaotic system which has only one equilibrium. There are only 8 terms in all four equations of the new hyper-chaotic system, which may be less than any other four-dimensional continuous autonomous hyper-chaotic systems generated by three-dimensional (3D) continuous autonomous chaotic systems. The hyper-chaotic system undergoes Hopf bifurcation when parameter c varies, and becomes the 3D modified Lü system when parameter k varies. Although the hyper-chaotic system does not undergo Hopf bifurcation when parameter k varies, many dynamic behaviours such as periodic attractor, quasi periodic attractor, chaotic attractor and hyper-chaotic attractor can be observed. A circuit is also designed when parameter k varies and the results of the circuit experiment are in good agreement with those of simulation.

Abstract: By introducing an additional state feedback into a three-dimensional autonomous chaotic attractor Lü system, this paper presents a novel four-dimensional continuous autonomous hyper-chaotic system which has only one equilibrium. There are only 8 terms in all four equations of the new hyper-chaotic system, which may be less than any other four-dimensional continuous autonomous hyper-chaotic systems generated by three-dimensional (3D) continuous autonomous chaotic systems. The hyper-chaotic system undergoes Hopf bifurcation when parameter c varies, and becomes the 3D modified Lü system when parameter k varies. Although the hyper-chaotic system does not undergo Hopf bifurcation when parameter k varies, many dynamic behaviours such as periodic attractor, quasi periodic attractor, chaotic attractor and hyper-chaotic attractor can be observed. A circuit is also designed when parameter k varies and the results of the circuit experiment are in good agreement with those of simulation.

Key words: hyper-chaotic, bifurcation, circuit implementation, Lyapunov exponents

中图分类号: (High-dimensional chaos)

05.45.Jn

05.45.Gg (Control of chaos, applications of chaos) 02.30.Oz (Bifurcation theory)

贾红艳, 陈增强, 袁著祉. A novel one equilibrium hyper-chaotic system generated upon Lü attractor[J]. 中国物理B, 2010, 19(2): 20507-020507.

Jia Hong-Yan(贾红艳), Chen Zeng-Qiang(陈增强), and Yuan Zhu-Zhi(袁著祉). A novel one equilibrium hyper-chaotic system generated upon Lü attractor[J]. Chin. Phys. B, 2010, 19(2): 20507-020507.

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A novel one equilibrium hyper-chaotic system generated upon Lü attractor

A novel one equilibrium hyper-chaotic system generated upon Lü attractor

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