分数阶混沌系统与整数阶混沌系统之间的同步

周平; 邝菲

doi:10.7498/aps.59.6851

摘要

基于追踪控制的思想,利用分数阶系统稳定性理论,实现了分数阶混沌系统与整数阶混沌系统之间的混沌同步,给出了补偿器和反馈控制器的选择方法. 以三维分数阶Chen系统和三维整数阶Lorenz混沌系统之间的混沌同步为例进行了数值仿真和电路仿真. 研究表明了该同步方法的有效性.

关键词:

Based on the idea of tracking control and the stability theory of linear fractional-order system, chaotic synchronization between fractional-order chaotic system and chaotic system of integer orders is proposed. A compensation controller and a feedback controller are given. Synchronization between the fractional-order Chen chaotic system and the Loren chaotic system of integer orders is used to illustrate the effectiveness of the proposed synchronization approach. Numerical and circuit simulations coincide with the theoretical analysis.

Keywords:

作者及机构信息

周平,
邝菲

1.
重庆邮电大学应用物理研究所,重庆 400065

Authors and contacts

1.
Institute of Applied Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

参考文献

[1]	Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2]	Li Z G, Xu D L 2001 Phys. Lett. A 282 175
[3]	Lu J Q, Xi Y G 2003 Chaos Soliton Fract. 17 825
[4]	Zou Y L, Zhu J 2006 Chin. Phys. 15 1965
[5]	Lǔ L, Luan L, Guo Z A 2007 Chin. Phys. 16 346
[6]	Liu Y Z, Jiang C S, Lin C S 2007 Acta Phys. Sin. 56 707 (in Chinese)[刘扬正、姜长圣、林长圣 2007 物理学报 56 707]
[7]	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]
[8]	Gao X, Yu J B 2005 Chin. Phys. 14 908
[9]	Grigorenko I, Grigorenko E 2003 Phys. Rev. Lett. 91 034101
[10]	Li C G, Chen G 2004 Physica A 341 55
[11]	Ahmad W M, Sprott J C 2003 Chaos Soliton Fract. 16 339
[12]	Li C G, Liao X F, Yu J B 2003 Phys. Rev. E 68 067203
[13]	Zhou P 2007 Chin. Phys. 16 1263
[14]	Peng G J, Jiang Y L 2008 Phys. Lett. A 372 3963
[15]	Chen X R, Liu C X, Li Y X 2008 Acta Phys. Sin. 57 (in Chinese) 1453[陈向荣、刘崇新、李永勋 2008 物理学报 57 1453]
[16]	Peng G J, Jiang Y L, Chen F 2008 Physica A 387 3738
[17]	Shao S Q 2009 Chaos Soliton. Fract. 39 1572
[18]	Zhou P, Wei L J, Cheng X F 2009 Chin. Phys. B 18 2674
[19]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[20]	Chen G, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[21]	Mohammad S T, Mohammad H 2007 Phys. Lett. A 367 102
[22]	Wang X Y, Shi Q J 2005 Acta Phys. Sin. 54 5591 (in Chinese) [王兴元、石其江 2005 物理学报 54 5591]
[23]	Min F H, Wang Z Q 2008 Acta Phys. Sin. 57 31 (in Chinese) [闵富红、王执铨 2008 物理学报 57 31]
[24]	Li C L, Luo X S 2009 Acta Phys. Sin. 58 3759 (in Chinese) [李春来、罗晓曙 2009 物理学报 58 3759]
[25]	Liu J J, Liu C X 2007 Chin. Phys. 16 1586
[26]	Wang F Q, Liu C X 2006 Acta Phys. Sin.  55 3922 (in Chinese) [王发强、刘崇新 2006 物理学报 55 3922]

施引文献

[1]	Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2]	Li Z G, Xu D L 2001 Phys. Lett. A 282 175
[3]	Lu J Q, Xi Y G 2003 Chaos Soliton Fract. 17 825
[4]	Zou Y L, Zhu J 2006 Chin. Phys. 15 1965
[5]	Lǔ L, Luan L, Guo Z A 2007 Chin. Phys. 16 346
[6]	Liu Y Z, Jiang C S, Lin C S 2007 Acta Phys. Sin. 56 707 (in Chinese)[刘扬正、姜长圣、林长圣 2007 物理学报 56 707]
[7]	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]
[8]	Gao X, Yu J B 2005 Chin. Phys. 14 908
[9]	Grigorenko I, Grigorenko E 2003 Phys. Rev. Lett. 91 034101
[10]	Li C G, Chen G 2004 Physica A 341 55
[11]	Ahmad W M, Sprott J C 2003 Chaos Soliton Fract. 16 339
[12]	Li C G, Liao X F, Yu J B 2003 Phys. Rev. E 68 067203
[13]	Zhou P 2007 Chin. Phys. 16 1263
[14]	Peng G J, Jiang Y L 2008 Phys. Lett. A 372 3963
[15]	Chen X R, Liu C X, Li Y X 2008 Acta Phys. Sin. 57 (in Chinese) 1453[陈向荣、刘崇新、李永勋 2008 物理学报 57 1453]
[16]	Peng G J, Jiang Y L, Chen F 2008 Physica A 387 3738
[17]	Shao S Q 2009 Chaos Soliton. Fract. 39 1572
[18]	Zhou P, Wei L J, Cheng X F 2009 Chin. Phys. B 18 2674
[19]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[20]	Chen G, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[21]	Mohammad S T, Mohammad H 2007 Phys. Lett. A 367 102
[22]	Wang X Y, Shi Q J 2005 Acta Phys. Sin. 54 5591 (in Chinese) [王兴元、石其江 2005 物理学报 54 5591]
[23]	Min F H, Wang Z Q 2008 Acta Phys. Sin. 57 31 (in Chinese) [闵富红、王执铨 2008 物理学报 57 31]
[24]	Li C L, Luo X S 2009 Acta Phys. Sin. 58 3759 (in Chinese) [李春来、罗晓曙 2009 物理学报 58 3759]
[25]	Liu J J, Liu C X 2007 Chin. Phys. 16 1586
[26]	Wang F Q, Liu C X 2006 Acta Phys. Sin.  55 3922 (in Chinese) [王发强、刘崇新 2006 物理学报 55 3922]

计量

文章访问数: 7765
PDF下载量: 1314
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