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Symbolic dynamics, which partitions the infinite number of finite length trajectories into a finite number of trajectory sets, allows a simplified and "coarse-grained" description of the dynamics of a system with a limited number of symbols. In this paper, we further develop the symbolic vector dynamical estimation method in coupled map lattice (CML). We take the CML of Logistic map as an example, to show that the control parameters affect the dynamical characters of symbolic vector sequence. We study the ergodic property of CML by using the inverse function of CML. We give the symbolic vector dynamical description of the initial values, the forbidden words and the control parameters for studying pattern formation in CML. We also give a coupling coefficient estimation approach based on the ergodic property.
[1] Hao B L 1994 Starting With Parabolas2An Introduction to Chaotic Dynamics ( Shnghai : Shanghai Seientific and Technological Education Publishing House) (in Chinese) [郝柏林1994 从抛物线谈起——混沌动力学引论(上海科学技术教育出版社)]
[2] Zheng WM, Hao B L 1994 Applied Symbolic Dynamics (Shnghai : Shanghai Seientific and Technological Education Publishing House) (in Chinese) [郑伟谋、郝柏林 1994 实用符号动力学(上海科学技术教育出版社) ]
[3] Wu XG, Hu H P, Zhang B 2004 Chaos Solition. Fract. 22 359
[4] Alvarez G, Montoya F, Romera M and Pastor G C 2003 Phys. Lett. A 311 172
[5] Ling C, Wu X F, Sun S G 1999 IEEE Trans. Signal Proc. 47 1424
[6] Yang W M 1994 Spatiotemporal Chaos and Coupled Map Lattice ( Shnghai : Shanghai Seientific and Technological Education Publishing House) (in Chinese) [杨维明1994 时空混沌和耦 合映象格子(上海科学技术教育出版社) ] 〖7] Coutinho R, Femandez B 1997 Physica D108 60
[7] Shawn D P, Ned J C, Erik B 2006 Phys. Rev. Lett. 96 034105
[8] Shawn D P, Ned J C, Erik B, 2007 Phys. Rev. Lett. 99 214101
[9] Zeng Y C, Tong Q Y 2003 Acta Phys. Sin. 52 285 (in Chinese) [曾以成、童勤业 2003 物理学报 52 285 ]
[10] Liu Y, Shen M F, Chen H Y 2006 Acta Phys. Sin. 55 564 (in Chinese) [刘 英、沈民奋、陈和晏 2006 物理学报 55 564]
[11] Wang K, Pei W J, Xia H S, He Z Y 2007 Acta Phys. Sin. 56 3766 (in Chinese) [王 开、裴文江、何振亚 2007 物理学报 56 3766]
[12] Kang W, Pei W J, Wang S P, Cheung Y M, He Z Y 2008 IEEE Trans. Circuits Syst. I 55 1116
[13] Kang W, Pei W J, Wang S P, He Z Y, Cheung Y M 2007 Phys. Lett. A 367 316
[14] Kang W, Pei W J, Wang S P, Cheung Y M, Shen Y, He Z Y 2010 Phys. Lett. A 374 562
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[1] Hao B L 1994 Starting With Parabolas2An Introduction to Chaotic Dynamics ( Shnghai : Shanghai Seientific and Technological Education Publishing House) (in Chinese) [郝柏林1994 从抛物线谈起——混沌动力学引论(上海科学技术教育出版社)]
[2] Zheng WM, Hao B L 1994 Applied Symbolic Dynamics (Shnghai : Shanghai Seientific and Technological Education Publishing House) (in Chinese) [郑伟谋、郝柏林 1994 实用符号动力学(上海科学技术教育出版社) ]
[3] Wu XG, Hu H P, Zhang B 2004 Chaos Solition. Fract. 22 359
[4] Alvarez G, Montoya F, Romera M and Pastor G C 2003 Phys. Lett. A 311 172
[5] Ling C, Wu X F, Sun S G 1999 IEEE Trans. Signal Proc. 47 1424
[6] Yang W M 1994 Spatiotemporal Chaos and Coupled Map Lattice ( Shnghai : Shanghai Seientific and Technological Education Publishing House) (in Chinese) [杨维明1994 时空混沌和耦 合映象格子(上海科学技术教育出版社) ] 〖7] Coutinho R, Femandez B 1997 Physica D108 60
[7] Shawn D P, Ned J C, Erik B 2006 Phys. Rev. Lett. 96 034105
[8] Shawn D P, Ned J C, Erik B, 2007 Phys. Rev. Lett. 99 214101
[9] Zeng Y C, Tong Q Y 2003 Acta Phys. Sin. 52 285 (in Chinese) [曾以成、童勤业 2003 物理学报 52 285 ]
[10] Liu Y, Shen M F, Chen H Y 2006 Acta Phys. Sin. 55 564 (in Chinese) [刘 英、沈民奋、陈和晏 2006 物理学报 55 564]
[11] Wang K, Pei W J, Xia H S, He Z Y 2007 Acta Phys. Sin. 56 3766 (in Chinese) [王 开、裴文江、何振亚 2007 物理学报 56 3766]
[12] Kang W, Pei W J, Wang S P, Cheung Y M, He Z Y 2008 IEEE Trans. Circuits Syst. I 55 1116
[13] Kang W, Pei W J, Wang S P, He Z Y, Cheung Y M 2007 Phys. Lett. A 367 316
[14] Kang W, Pei W J, Wang S P, Cheung Y M, Shen Y, He Z Y 2010 Phys. Lett. A 374 562
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