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A three-dimensional chaotic system is presented. The equilibrium point, the chaotic attractor and the Lyapunov exponent are investigated. According to the chaotic system, we propose a novel chaos synchronization method in which only the amplitude of chaotic signal is used to realize chaos synchronization. This feature can be used in chaotic communication system to improve the communication quality and speed. By computing the conditional Lyapunov exponents and numerical simulation the synchronization method is proved to be feasible and effective. The synchronous speed of the method is the same as that of the traditional linear feedback method.
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Keywords:
- three-dimensional chaos /
- chaos synchronization /
- conditional Lyapunov exponents /
- chaotic communication
[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Maggio G M, di Bernardo M, Kennedy M P 2000 IEEE Trans. Circuits Syst. Ⅰ 47 1160
[3] Lu J G 2005 Chaos Solitons Fract. 26 1125
[4] Kocarev L, Parlitz V 1995 Phys. Rev. Lett. 74 5028
[5] Bai E W, Lonngen K E 2000 Chaos Solitons Fract. 11 1041
[6] Agiza H N, Yassen M T 2001 Phys. Lett. A 278 191
[7] Wang G R, Yu X L, Chen S G 2000 Control, Synchronization and Utilization of Chaos (Beijing: National Defense Industry Press) p354 (in Chinese) [王光瑞, 于熙龄, 陈式刚 2000 混沌的控制、同步与利用 (北京: 国防工业出版社) 第354页]
[8] Wang X Y, Meng J 2008 Acta Phys. Sin. 57 726 (in Chinese) [王兴元, 孟娟 2008 物理学报 57 726]
[9] Zhang R X, Yang S P, Liu Y L 2010 Acta Phys. Sin. 59 1549 (in Chinese) [张若洵, 杨世平, 刘永利 2010 物理学报 59 1549]
[10] Huberman B A, Lumer E 1990 IEEE Trans. Circuits Syst. 37 547
[11] Andrievsky B 2002 Math. Comput. Sim. 58 285
[12] Hu J, Zhang Q J 2008 Chin. Phys. B 17 503
[13] Steliana C 2003 Chaos Solitons Fract. 15 507
[14] Cai N, Jing Y W, Zhang S Y 2009 Acta Phys. Sin. 58 802 (in Chinese) [蔡娜, 井元伟, 张嗣瀛 2009 物理学报 58 802]
[15] Wu X J, Lu H T, Shen S L 2009 Phys. Lett. A 373 2329
[16] Fu S H, Pei L J 2010 Acta Phys. Sin. 59 5985 (in Chinese) [付士慧, 裴利军 2010 物理学报 59 5985]
[17] Chen M, Jiang C S, Jiang B, Wu Q X 2009 Chaos Sloitons Fract. 39 1856
[18] Liu Z H 2006 Basic and Application of Chaotic Dynamics (Beijing: Higher Education Press) p28 (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28页]
[19] Fang J Q 2001 Manage Chaos and Develop High and New Technology (Beijing: Atomic Energy Press) p35 (in Chinese) [方锦清 2001 驾驭混沌与发展高新技术 (北京: 原子能出版社) 第35页]
[20] Yi K X, Sun X, Shi J Y 2000 J. CAD CG 12 672 (in Chinese) [易开祥, 孙鑫, 石教英 2000 计算机辅助设计与图形学报 12 672]
[21] Zhang X D, Li Z P, Zhang L L 2005 J. Univ. Sci. Technol. Beijing 27 371 (in Chinese) [张晓丹, 李志萍, 张丽丽 2005 北京科技大学学报 27 371]
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[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Maggio G M, di Bernardo M, Kennedy M P 2000 IEEE Trans. Circuits Syst. Ⅰ 47 1160
[3] Lu J G 2005 Chaos Solitons Fract. 26 1125
[4] Kocarev L, Parlitz V 1995 Phys. Rev. Lett. 74 5028
[5] Bai E W, Lonngen K E 2000 Chaos Solitons Fract. 11 1041
[6] Agiza H N, Yassen M T 2001 Phys. Lett. A 278 191
[7] Wang G R, Yu X L, Chen S G 2000 Control, Synchronization and Utilization of Chaos (Beijing: National Defense Industry Press) p354 (in Chinese) [王光瑞, 于熙龄, 陈式刚 2000 混沌的控制、同步与利用 (北京: 国防工业出版社) 第354页]
[8] Wang X Y, Meng J 2008 Acta Phys. Sin. 57 726 (in Chinese) [王兴元, 孟娟 2008 物理学报 57 726]
[9] Zhang R X, Yang S P, Liu Y L 2010 Acta Phys. Sin. 59 1549 (in Chinese) [张若洵, 杨世平, 刘永利 2010 物理学报 59 1549]
[10] Huberman B A, Lumer E 1990 IEEE Trans. Circuits Syst. 37 547
[11] Andrievsky B 2002 Math. Comput. Sim. 58 285
[12] Hu J, Zhang Q J 2008 Chin. Phys. B 17 503
[13] Steliana C 2003 Chaos Solitons Fract. 15 507
[14] Cai N, Jing Y W, Zhang S Y 2009 Acta Phys. Sin. 58 802 (in Chinese) [蔡娜, 井元伟, 张嗣瀛 2009 物理学报 58 802]
[15] Wu X J, Lu H T, Shen S L 2009 Phys. Lett. A 373 2329
[16] Fu S H, Pei L J 2010 Acta Phys. Sin. 59 5985 (in Chinese) [付士慧, 裴利军 2010 物理学报 59 5985]
[17] Chen M, Jiang C S, Jiang B, Wu Q X 2009 Chaos Sloitons Fract. 39 1856
[18] Liu Z H 2006 Basic and Application of Chaotic Dynamics (Beijing: Higher Education Press) p28 (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28页]
[19] Fang J Q 2001 Manage Chaos and Develop High and New Technology (Beijing: Atomic Energy Press) p35 (in Chinese) [方锦清 2001 驾驭混沌与发展高新技术 (北京: 原子能出版社) 第35页]
[20] Yi K X, Sun X, Shi J Y 2000 J. CAD CG 12 672 (in Chinese) [易开祥, 孙鑫, 石教英 2000 计算机辅助设计与图形学报 12 672]
[21] Zhang X D, Li Z P, Zhang L L 2005 J. Univ. Sci. Technol. Beijing 27 371 (in Chinese) [张晓丹, 李志萍, 张丽丽 2005 北京科技大学学报 27 371]
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