时滞复Lorenz混沌系统特性及其自时滞同步

张芳芳; 刘树堂; 余卫勇

doi:10.7498/aps.62.220505

摘要

自时滞同步是指保持混沌系统结构和参数不变的情况下, 使时滞系统和原系统同步, 从而避免了现实中因为时滞而产生的各种问题. 本文以时滞复Lorenz系统为例, 研究其动态特性及时滞因数的影响, 并提出了一种非线性反馈控制器实现了复Lorenz系统的自时滞混沌同步. 数值仿真结果验证了该控制器的有效性. 该控制器只对部分状态进行控制, 实现了所有状态的同步, 原理简单, 易于工程实现.

关键词:

Self-synchronization of time delay implies that the synchronization between the time-delay system and the original system keeps the structure and parameters of systems unchanged, thus these various problems produced by time-delay in practice are avoided. Taking a time-delay complex Lorenz system for example, we investigate its dynamic characteristics and the influence of of time lag factor. A nonlinear feedback controller is designed to realize the self-synchronization of time delay of the complex Lorenz system. Numerical simulations verify the effectiveness of the presented controller. The controller adopts some states to realize the synchronization of all states. It is simple in principle and easy to implement in engineering.

Keywords:

作者及机构信息

1.
山东大学控制科学与工程学院, 济南 250061

基金项目: 国家自然科学基金(批准号: 61273088, 10971120, 61001099)和山东省自然科学基金(批准号: ZR2010FM010)资助的课题.

Authors and contacts

1.
College of Control Science and Engineering, Shandong University, Jinan 250061, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61273088, 10971120, 61001099) and the Nature Science Foundation of Shandong Province, China (Grant No. ZR2010FM010).

参考文献

[1]	Liang Y, Wang X Y 2013 Acta Phys. Sin. 62 018901 (in Chinese) [梁义, 王兴元 2013 62 018901]
[2]	Ouyang C, Lin W T, Cheng R J, Mo J Q 2013 Acta Phys. Sin. 62 060201 (in Chinese) [欧阳成, 林万涛, 程荣军, 莫嘉琪 2013 62 060201]
[3]	Li C D, Liao X F 2004 Phys. Lett. A 329 301
[4]	Jia F L, Xu W 2007 Acta Phys. Sin. 56 3101 (in Chinese) [贾飞蕾, 徐伟 2007 56 3101]
[5]	Mahmoud G M, Mahmoud E E 2012 Nonlinear Dyn. 67 1613
[6]	Wang X Y, Zhang H 2013 Chin. Phys. B 22 048902
[7]	Fowler A C, Gibbon J D 1982 Physica D 4 139
[8]	Mahmoud G M, Bountis T, Mahmoud E E 2007 Internat. J. Bifur. Chaos 17 4295
[9]	Luo C, Wang X Y 2013 Nonlinear Dyn. 71 241
[10]	Luo C, Wang X Y 2013 Int. J. Mod. Phys. C 24 1350025
[11]	Mahmoud G M, Mahmoud E E 2010 Nonlinear Dyn. 61 141
[12]	Nian F Z, Wang X Y, Niu Y J, Lin D 2010 Appl. Math. Comput. 217 2481
[13]	Mahmoud G M, Mahmoud E E 2010 Nonlinear Dyn. 62 875
[14]	Liu S T, Liu P 2011 Nonlinear Anal. Real 12 3046
[15]	Liu P, Liu S T 2011 Phys. Scr. 83 065006
[16]	Mahmoud G M, Mahmoud E E 2010 Math. Comput. Simulat. 80 2286
[17]	Liu P, Liu S 2012 Nonlinear Dyn. 70 585
[18]	Zhu H 2011 ICCRD: 3rd Int. Conf. on Computer Research Development Shanghai, China, March 11–13, 2011 p451
[19]	Liu P, Liu S T, Li X 2012 Phys. Scr. 85 035005
[20]	Mahmoud E E 2013 Math. Comput. Simulat. 89 69
[21]	Zhang F F, Liu S T, Yu W Y 2013 Chin. Phys. B 22 120505
[22]	Gibbon J D, McGuinnes M J 1982 Physica D 5 108
[23]	Ning C Z, Haken H 1990 Phys. Rev. A 41 3826
[24]	Rauh A, Hannibal L, Abraham N 1996 Physica D 99 45
[25]	Richter H 2001 Chaos Soliton. Fract. 12 2375
[26]	Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285
[27]	Hale J 1977 Theory of Functional Differential Equations (Vol. 3) (Berlin: Springer-Verlag) pp1–244

施引文献

[1]	Liang Y, Wang X Y 2013 Acta Phys. Sin. 62 018901 (in Chinese) [梁义, 王兴元 2013 62 018901]
[2]	Ouyang C, Lin W T, Cheng R J, Mo J Q 2013 Acta Phys. Sin. 62 060201 (in Chinese) [欧阳成, 林万涛, 程荣军, 莫嘉琪 2013 62 060201]
[3]	Li C D, Liao X F 2004 Phys. Lett. A 329 301
[4]	Jia F L, Xu W 2007 Acta Phys. Sin. 56 3101 (in Chinese) [贾飞蕾, 徐伟 2007 56 3101]
[5]	Mahmoud G M, Mahmoud E E 2012 Nonlinear Dyn. 67 1613
[6]	Wang X Y, Zhang H 2013 Chin. Phys. B 22 048902
[7]	Fowler A C, Gibbon J D 1982 Physica D 4 139
[8]	Mahmoud G M, Bountis T, Mahmoud E E 2007 Internat. J. Bifur. Chaos 17 4295
[9]	Luo C, Wang X Y 2013 Nonlinear Dyn. 71 241
[10]	Luo C, Wang X Y 2013 Int. J. Mod. Phys. C 24 1350025
[11]	Mahmoud G M, Mahmoud E E 2010 Nonlinear Dyn. 61 141
[12]	Nian F Z, Wang X Y, Niu Y J, Lin D 2010 Appl. Math. Comput. 217 2481
[13]	Mahmoud G M, Mahmoud E E 2010 Nonlinear Dyn. 62 875
[14]	Liu S T, Liu P 2011 Nonlinear Anal. Real 12 3046
[15]	Liu P, Liu S T 2011 Phys. Scr. 83 065006
[16]	Mahmoud G M, Mahmoud E E 2010 Math. Comput. Simulat. 80 2286
[17]	Liu P, Liu S 2012 Nonlinear Dyn. 70 585
[18]	Zhu H 2011 ICCRD: 3rd Int. Conf. on Computer Research Development Shanghai, China, March 11–13, 2011 p451
[19]	Liu P, Liu S T, Li X 2012 Phys. Scr. 85 035005
[20]	Mahmoud E E 2013 Math. Comput. Simulat. 89 69
[21]	Zhang F F, Liu S T, Yu W Y 2013 Chin. Phys. B 22 120505
[22]	Gibbon J D, McGuinnes M J 1982 Physica D 5 108
[23]	Ning C Z, Haken H 1990 Phys. Rev. A 41 3826
[24]	Rauh A, Hannibal L, Abraham N 1996 Physica D 99 45
[25]	Richter H 2001 Chaos Soliton. Fract. 12 2375
[26]	Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285
[27]	Hale J 1977 Theory of Functional Differential Equations (Vol. 3) (Berlin: Springer-Verlag) pp1–244

[1]	马召召, 杨庆超, 周瑞平. 一种基于摄动理论的不连续系统Lyapunov指数算法. , 2021, 70(24): 240501. doi: 10.7498/aps.70.20210492
[2]	李清都, 郭建丽. 切换系统Lyapunov指数的算法及应用. , 2014, 63(10): 100501. doi: 10.7498/aps.63.100501
[3]	周小勇, 乔晓华, 朱雷, 刘素芬. 一类关联混沌系统及其切换与内同步机理研究. , 2013, 62(19): 190504. doi: 10.7498/aps.62.190504
[4]	张毅, 金世欣. 含时滞的非保守系统动力学的Noether对称性. , 2013, 62(23): 234502. doi: 10.7498/aps.62.234502
[5]	郝建红, 孙娜燕. 损耗型变形耦合电机系统的混沌参数特性. , 2012, 61(15): 150504. doi: 10.7498/aps.61.150504
[6]	刘扬正, 林长圣, 李心朝. 切换统一混沌系统族. , 2011, 60(4): 040505. doi: 10.7498/aps.60.040505
[7]	刘扬正, 林长圣, 李心朝, 刘海鹏, 王忠林. Logistic-Unified混杂混沌系统. , 2011, 60(3): 030502. doi: 10.7498/aps.60.030502
[8]	许喆, 刘崇新, 杨韬. 一种新型混沌系统的分析及电路实现. , 2010, 59(1): 131-139. doi: 10.7498/aps.59.131
[9]	唐良瑞, 李静, 樊冰. 一个新四维自治超混沌系统及其电路实现. , 2009, 58(3): 1446-1455. doi: 10.7498/aps.58.1446
[10]	刘扬正, 姜长生. 关联可切换超混沌系统的构建与特性分析. , 2009, 58(2): 771-778. doi: 10.7498/aps.58.771
[11]	唐良瑞, 李静, 樊冰, 翟明岳. 新三维混沌系统及其电路仿真. , 2009, 58(2): 785-793. doi: 10.7498/aps.58.785
[12]	刘明华, 冯久超. 一个新的超混沌系统. , 2009, 58(7): 4457-4462. doi: 10.7498/aps.58.4457
[13]	于思瑶, 郭树旭, 郜峰利. 半导体激光器低频噪声的Lyapunov指数计算和混沌状态判定. , 2009, 58(8): 5214-5217. doi: 10.7498/aps.58.5214
[14]	刘勇. 耦合系统的混沌相位同步. , 2009, 58(2): 749-755. doi: 10.7498/aps.58.749
[15]	张勇, 关伟. 基于最大Lyapunov指数的多变量混沌时间序列预测. , 2009, 58(2): 756-763. doi: 10.7498/aps.58.756
[16]	张晓丹, 刘翔, 赵品栋. 一类延迟混沌系统沿主轴方向上Lyapunov指数的计算方法. , 2009, 58(7): 4415-4420. doi: 10.7498/aps.58.4415
[17]	张琪昌, 田瑞兰, 王炜. 一类机电耦合非线性动力系统的混沌动力学特征. , 2008, 57(5): 2799-2804. doi: 10.7498/aps.57.2799
[18]	刘扬正, 姜长生, 林长圣, 孙晗. 四维切换超混沌系统. , 2007, 56(9): 5131-5135. doi: 10.7498/aps.56.5131
[19]	王兴元, 王明军. 超混沌Lorenz系统. , 2007, 56(9): 5136-5141. doi: 10.7498/aps.56.5136
[20]	包刚, 那仁满都拉, 图布心, 额尔顿仓. 耦合混沌振子系统完全同步的动力学行为. , 2007, 56(4): 1971-1974. doi: 10.7498/aps.56.1971

计量

文章访问数: 6955
PDF下载量: 849
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板