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A novel three-dimensional chaotic system with invariable Lyapunov exponent is proposed. The new system contains six system parameters, one quadratic cross-product term, and one square term. The dynamic properties of the new system are investigated via theoretical analysis, numerical simulation, Lyapunov dimension, Poincare diagrams, Lyapunov exponent spectrum, and bifurcation diagrams. The different dynamic behaviors of the new system are analyzed when each system parameter is changed. When the parameter of the square term varies, the Lyapunov exponent spectrum keeps invariable, the amplitudes of the signals of the first two dimensions change each as a power function with a minus half index, but the third one keeps its amplitude in the same range. Finally, the circuit of this new chaotic system is designed and realized by Multisim software, which confirms that the chaotic system can be achieved.
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Keywords:
- chaotic system /
- invariable Lyapunov exponent spectrum /
- Poincare diagrams /
- chaotic circuit
[1] Lorenz E N 1963 J.Atmos.Sci.20 130
[2] Lorenz E N 1993 The Essence of Chaos(Washington:University of Washington Press)
[3] [4] [5] Chen G R,Ueta T 1999 Int.J.Bifur.Chaos 9 1465
[6] Celikovsky S,Chen G R 2002 Int.J.Bifur.Chaos 12 1789
[7] [8] L J H,Chen G R 2002 Int.J.Bifur.Chaos 12 659
[9] [10] [11] L J H,Chen G R,Cheng D Z 2002 Int.J.Bifur.Chaos 12 2917
[12] [13] Chen G R,L J H 2003 Dynamics of the Lorenz System Family:Analysis,Control and Synchronization (Beijing: Science Press) p150 (in Chinese) [陈关荣、吕金虎 2003 Lorenz系统族的动 力学分析、控制与同步(北京:科学出版社)第150页] 〖8] Liu C X,Liu L,Liu K 2004 Chaos Soliton.Fract.22 1031
[14] [15] [16] Tang L R, Li J, Fan B 2009 Acta Phys.Sin.58 785(in Chinese) [唐良瑞、李 静、樊 冰 2009 物理学报 58 785]
[17] Cai G L,Zheng S,Tian L X 2008 Chin. Phys. B 17 4039
[18] [19] Liu C X,Liu L 2009 Chin. Phys. B 18 2188
[20] [21] [22] Li C B,Wang H K,Chen S 2010 Acta Phys.Sin.59 0783(in Chinese) [李春彪、王翰康、陈 谡 2010 物理学报 59 783]
[23] Liu Z H 2006 Fundamentals and Applications of Chaotic Dynamics(Beijing:High Educatioin Press) p18 (in Chinese)[刘宗华 2006 混沌动力学基础及其应用(北京:高等教育出版社)第18页]
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[1] Lorenz E N 1963 J.Atmos.Sci.20 130
[2] Lorenz E N 1993 The Essence of Chaos(Washington:University of Washington Press)
[3] [4] [5] Chen G R,Ueta T 1999 Int.J.Bifur.Chaos 9 1465
[6] Celikovsky S,Chen G R 2002 Int.J.Bifur.Chaos 12 1789
[7] [8] L J H,Chen G R 2002 Int.J.Bifur.Chaos 12 659
[9] [10] [11] L J H,Chen G R,Cheng D Z 2002 Int.J.Bifur.Chaos 12 2917
[12] [13] Chen G R,L J H 2003 Dynamics of the Lorenz System Family:Analysis,Control and Synchronization (Beijing: Science Press) p150 (in Chinese) [陈关荣、吕金虎 2003 Lorenz系统族的动 力学分析、控制与同步(北京:科学出版社)第150页] 〖8] Liu C X,Liu L,Liu K 2004 Chaos Soliton.Fract.22 1031
[14] [15] [16] Tang L R, Li J, Fan B 2009 Acta Phys.Sin.58 785(in Chinese) [唐良瑞、李 静、樊 冰 2009 物理学报 58 785]
[17] Cai G L,Zheng S,Tian L X 2008 Chin. Phys. B 17 4039
[18] [19] Liu C X,Liu L 2009 Chin. Phys. B 18 2188
[20] [21] [22] Li C B,Wang H K,Chen S 2010 Acta Phys.Sin.59 0783(in Chinese) [李春彪、王翰康、陈 谡 2010 物理学报 59 783]
[23] Liu Z H 2006 Fundamentals and Applications of Chaotic Dynamics(Beijing:High Educatioin Press) p18 (in Chinese)[刘宗华 2006 混沌动力学基础及其应用(北京:高等教育出版社)第18页]
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