通过同步实现"有序+有序=混沌"的例子

张荣; 徐振源; 杨永清

doi:10.7498/aps.60.010515

摘要

研究了连续的混沌系统是否存在"有序+有序=混沌"的现象,研究表明两个吸引子为周期运动的动力学系统经双向耦合达到同步后,同步后的系统可产生混沌态.采用特定参数下的Lorenz系统和Rssler系统作为例子,对连续的动力系统给出了一个"有序+有序=混沌"的例子.

关键词:

混沌 /
有序 /
耦合 /
同步

It was investigated whether the phenomenon of "order+order=chaos" exists for chaotic continuous systems. It was shown that the bidirectional coupling of two ordered continuous dynamics can originate a chaotic dynamics via synchronization. We provide an explicit example of "order+order=chaos" by taking the Lorenz and Rssler systems in their periodic dynamics.

Keywords:

chaos /
order /
coupling /
synchronization

作者及机构信息

1.
江南大学理学院,无锡 214122

基金项目: 国家自然科学基金(批准号:60875036),江南大学创新团队发展计划资助的课题.

Authors and contacts

1.
School of Science,Jiangnan University,Wuxi 214122, China

参考文献

[1]	Schaffer W M 1985 Ecology 66(1) 93
[2]	Tufillaro N B, Ramshankar R, Gollub J P 1989 Phys. Rev. Lett. 62 422
[3]	Curry J H, Herring J R, JosipLoncaric J, Orszag S A 1984 Journal of Fluid Mechanics 147 1
[4]	Imbihl R 2001 Chin. Phys. 10124
[5]	Chen W Q, Hai W H, Li H, Ma Z Y 2007 Acta. Phys. Sin. 56 1305 (in Chinese) [陈文钦、海文华、李辉、马志英 2007 物理学报 56 1305 Yu S M, Zhang C X 2009 Acta. Phys. Sin. 58 120 (in Chinese) 〖禹思敏、张朝霞2009 物理学报 58 120]
[6]	Danilo P M, Li Y, Yang B J, Yuan Y 2009 Chin. Phys. B 18 958
[7]	Bao B C, Hu W, Kang Z S, Xu J 2009 Acta. Phys. Sin. 58 1420 (in Chinese) [包伯成、胡文、康祝圣、许建 2009 物理学报 58 1420]
[8]	Hess B, Mikhailov A 1994 Science 264 (5156) 223
[9]	Sun Z Q 1992 Acta. Phys. Sin. 41 1987 (in Chinese) [孙宗琦 1992 物理学报 41 1987]
[10]	Peng J Z, Yu H Z 2008 Chin. Phys. B 17 3143
[11]	Hu G S 2009 Acta. Phys. Sin. 58 3734 (in Chinese) [胡国四 2009 物理学报 58 3734]
[12]	Liu N, Li J F, Wang T S 2009 Acta. Phys. Sin. 58 3772 (in Chinese) [柳宁、李俊峰、王天舒 2009 物理学报 58 3772]
[13]	Almeida J, Salasb D P, Romerac M 2005 Physica D 200 124
[14]	Xu F D, Luo J G, Liu Z R 2008 Comm. On Appl. Math. And Comput. 22(2) 35 (in Chinese) [徐凤丹、罗吉贵、刘曾荣 2008 应用数学与计算数学学报 22(2) 35]
[15]	Parrondo J M R, Harmer G P, Abbott D 2000 Phys. Rev. Lett. 85 5226
[16]	Harmer G P, Abbott D 1999 Stat. Sci. 14 206
[17]	Harmer G P, Abbott D 1999 Nature 402 864

施引文献

[1]	Schaffer W M 1985 Ecology 66(1) 93
[2]	Tufillaro N B, Ramshankar R, Gollub J P 1989 Phys. Rev. Lett. 62 422
[3]	Curry J H, Herring J R, JosipLoncaric J, Orszag S A 1984 Journal of Fluid Mechanics 147 1
[4]	Imbihl R 2001 Chin. Phys. 10124
[5]	Chen W Q, Hai W H, Li H, Ma Z Y 2007 Acta. Phys. Sin. 56 1305 (in Chinese) [陈文钦、海文华、李辉、马志英 2007 物理学报 56 1305 Yu S M, Zhang C X 2009 Acta. Phys. Sin. 58 120 (in Chinese) 〖禹思敏、张朝霞2009 物理学报 58 120]
[6]	Danilo P M, Li Y, Yang B J, Yuan Y 2009 Chin. Phys. B 18 958
[7]	Bao B C, Hu W, Kang Z S, Xu J 2009 Acta. Phys. Sin. 58 1420 (in Chinese) [包伯成、胡文、康祝圣、许建 2009 物理学报 58 1420]
[8]	Hess B, Mikhailov A 1994 Science 264 (5156) 223
[9]	Sun Z Q 1992 Acta. Phys. Sin. 41 1987 (in Chinese) [孙宗琦 1992 物理学报 41 1987]
[10]	Peng J Z, Yu H Z 2008 Chin. Phys. B 17 3143
[11]	Hu G S 2009 Acta. Phys. Sin. 58 3734 (in Chinese) [胡国四 2009 物理学报 58 3734]
[12]	Liu N, Li J F, Wang T S 2009 Acta. Phys. Sin. 58 3772 (in Chinese) [柳宁、李俊峰、王天舒 2009 物理学报 58 3772]
[13]	Almeida J, Salasb D P, Romerac M 2005 Physica D 200 124
[14]	Xu F D, Luo J G, Liu Z R 2008 Comm. On Appl. Math. And Comput. 22(2) 35 (in Chinese) [徐凤丹、罗吉贵、刘曾荣 2008 应用数学与计算数学学报 22(2) 35]
[15]	Parrondo J M R, Harmer G P, Abbott D 2000 Phys. Rev. Lett. 85 5226
[16]	Harmer G P, Abbott D 1999 Stat. Sci. 14 206
[17]	Harmer G P, Abbott D 1999 Nature 402 864

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