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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 Rssler systems in their periodic dynamics.
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Keywords:
- chaos /
- order /
- coupling /
- synchronization
[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 56 1305 Yu S M, Zhang C X 2009 Acta. Phys. Sin. 58 120 (in Chinese) 〖禹思敏、 张朝霞2009 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 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 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 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 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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[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 56 1305 Yu S M, Zhang C X 2009 Acta. Phys. Sin. 58 120 (in Chinese) 〖禹思敏、 张朝霞2009 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 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 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 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 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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