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参考Chen系统和Liu系统的构建模式, 对Lorenz系统进行改造, 构建一个新的三维自治混沌系统. 讨论了平衡点的性质, 给出了系统的功率谱图、 Poincare截面图, 并利用分岔图和Lyapunov指数谱详细分析了各参数变化对系统动力学行为的影响. 研究发现, 交叉乘积项参数d和平方项参数e变化时, 系统的Lyapunov指数谱保持恒定, 且参数d具有全局非线性调幅功能, 参数e具有局部非线性调幅功能. 另外, 设计了该混沌系统的模拟电路, 实验结果证实了混沌系统的可实现性.
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关键词:
- 混沌系统 /
- 恒Lyapunov指数谱 /
- 非线性调幅 /
- 电路实现
Based on the construction patterns of Chen and Liu chaotic systems, a new chaotic system is proposed by developing the Lorenz chaotic system. The essential features of chaotic system are analyzed via equilibrium, stability, continuous spectrum, and Poincare mapping. The different dynamic behaviors of the system are analyzed especially when each system parameter changes. It is found that when parameters d and e vary, the Lyapunov exponent spectrum keeps invariable, and there exist the functions of global nonlinear amplitude adjuster for d and partial nonlinear amplitude adjuster for e. Finally, a practical circuit is designed to implement this new chaotic system, which confirms that the chaotic system can be achieved physically.-
Keywords:
- chaotic system /
- invariable Lyapunov exponent spectrum /
- nonlinear amplitude adjuster /
- circuit implementation
[1] Lorenz E N 1963 J. Atmospheric Sci. 20 130
[2] Chen G R, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[3] [4] [5] L J H, Chen G 2002 Int. J. Bifur. Chaos 12 659
[6] [7] L J H, Chen G, Cheng D 2004 Int. J. Bifur. Chaos 14 1507
[8] [9] Liu W B, Chen G R 2003 Int. J. Bifur. Chaos 13 261
[10] Liu C X, Liu T, Liu L, Liu K 2004 Chaos Soliton. Fract. 22 1031
[11] [12] Qi G Y, Chen G R, Du S Z, Chen Z Q, Yuan Z Z 2005 Physica A 352 295
[13] [14] Hu G S 2009 Acta Phys. Sin. 58 8139 (in Chinese) [胡国四 2009 58 8139]
[15] [16] [17] Dong E Z, Chen Z P, Chen Z Q, Yuan Z Z 2009 Chin. Phys. B 18 2680
[18] [19] Wang H X, Cai G L, Miao S, Tian L X 2010 Chin. Phys. B 19 030509
[20] Si G Q, Cao H, Zhang Y B 2011 Chin. Phys. B 20 010509
[21] [22] [23] Jia H Y, Chen Z Q, Yuan Z Z 2010 Chin. Phys. B 19 020507
[24] [25] Luo X H 2009 Chin. Phys. B 18 3304
[26] [27] Liu M H, Feng J C, Tse C K 2010 Int. J. Bifur. Chaos 20 1201
[28] Li C B, Chen S, Zhu H Q 2009 Acta Phys. Sin. 58 2255 (in Chinese) [李春彪, 陈谡, 朱焕强 2009 58 2255]
[29] [30] [31] Li C B, Wang H K, Chen S 2010 Acta Phys. Sin. 59 783 (in Chinese) [李春彪, 王翰康, 陈谡 2010 59 783]
[32] Zhao P D, Zhang X D 2008 Acta Phys. Sin. 57 2791 (in Chinese) [赵品栋, 张晓丹 2008 57 2791]
[33] [34] 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]
[35] [36] Zhang X W 2009 High Frequency Electronics Circuit (Beijing: High Educatioin Press) p480 (in Chinese) [张肃文2009高频电子线路(北京: 高等教育出版社) 第480页]
[37] -
[1] Lorenz E N 1963 J. Atmospheric Sci. 20 130
[2] Chen G R, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[3] [4] [5] L J H, Chen G 2002 Int. J. Bifur. Chaos 12 659
[6] [7] L J H, Chen G, Cheng D 2004 Int. J. Bifur. Chaos 14 1507
[8] [9] Liu W B, Chen G R 2003 Int. J. Bifur. Chaos 13 261
[10] Liu C X, Liu T, Liu L, Liu K 2004 Chaos Soliton. Fract. 22 1031
[11] [12] Qi G Y, Chen G R, Du S Z, Chen Z Q, Yuan Z Z 2005 Physica A 352 295
[13] [14] Hu G S 2009 Acta Phys. Sin. 58 8139 (in Chinese) [胡国四 2009 58 8139]
[15] [16] [17] Dong E Z, Chen Z P, Chen Z Q, Yuan Z Z 2009 Chin. Phys. B 18 2680
[18] [19] Wang H X, Cai G L, Miao S, Tian L X 2010 Chin. Phys. B 19 030509
[20] Si G Q, Cao H, Zhang Y B 2011 Chin. Phys. B 20 010509
[21] [22] [23] Jia H Y, Chen Z Q, Yuan Z Z 2010 Chin. Phys. B 19 020507
[24] [25] Luo X H 2009 Chin. Phys. B 18 3304
[26] [27] Liu M H, Feng J C, Tse C K 2010 Int. J. Bifur. Chaos 20 1201
[28] Li C B, Chen S, Zhu H Q 2009 Acta Phys. Sin. 58 2255 (in Chinese) [李春彪, 陈谡, 朱焕强 2009 58 2255]
[29] [30] [31] Li C B, Wang H K, Chen S 2010 Acta Phys. Sin. 59 783 (in Chinese) [李春彪, 王翰康, 陈谡 2010 59 783]
[32] Zhao P D, Zhang X D 2008 Acta Phys. Sin. 57 2791 (in Chinese) [赵品栋, 张晓丹 2008 57 2791]
[33] [34] 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]
[35] [36] Zhang X W 2009 High Frequency Electronics Circuit (Beijing: High Educatioin Press) p480 (in Chinese) [张肃文2009高频电子线路(北京: 高等教育出版社) 第480页]
[37]
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