x

## 留言板

Parameter estimate from coupled map lattices based on symbolic vector dynamics

## Parameter estimate from coupled map lattices based on symbolic vector dynamics

Wang Kai, Pei Wen-Jiang, Zhang Yi-Feng, Zhou Si-Yuan, Shao Shuo
PDF

(PLEASE TRANSLATE TO ENGLISH

BY GOOGLE TRANSLATE IF NEEDED.)

• #### Abstract

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.

• Funds:

#### References

 [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

#### Cited By

•  [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
•  [1] Wang Kai, Pei Wen-Jiang, Xia Hai-Shan, He Zhen-Ya. Initial condition estimation from coupled map lattices based on symbolic vector dynamics. Acta Physica Sinica, 2007, 56(7): 3766-3770. doi: 10.7498/aps.56.3766 [2] Shen Min-Fen, Lin Lan-Xin, Li Xiao-Yan, Chang Chun-Qi. Initial condition estimate of coupled map lattices system based on symbolic dynamics. Acta Physica Sinica, 2009, 58(5): 2921-2929. doi: 10.7498/aps.58.2921 [3] Peng Xing-Zhao, Yao Hong, Du Jun, Ding Chao, Zhang Zhi-Hao. Study on cascading invulnerability of multi-coupling-links coupled networks based on time-delay coupled map lattices model. Acta Physica Sinica, 2014, 63(7): 078901. doi: 10.7498/aps.63.078901 [4] Liu Ying, Shen Min-Fen, Chan Francis H. Y.. Recovery of statistical property of initial conditions based on time-varying parameter from coupled map lattices. Acta Physica Sinica, 2006, 55(2): 564-571. doi: 10.7498/aps.55.564 [5] Cao Bao-Feng, Li Peng, Li Xiao-Qiang, Zhang Xue-Qin, Ning Wang-Shi, Liang Rui, Li Xin, Hu Miao, Zheng Yi. Detection and parameter estimation of weak pulse signal based on strongly coupled Duffing oscillators. Acta Physica Sinica, 2019, 68(8): 080501. doi: 10.7498/aps.68.20181856 [6] Song Jun-Qiang, Cao Xiao-Qun, Zhang Wei-Min, Zhu Xiao-Qian. Estimating parameters for coupled air-sea model with variational method. Acta Physica Sinica, 2012, 61(11): 110401. doi: 10.7498/aps.61.110401 [7] Liu Jian-Dong, Yu You-Ming. A TCML-based spatiotemporal chaotic one-way Hash function with changeable-parameter. Acta Physica Sinica, 2007, 56(3): 1297-1304. doi: 10.7498/aps.56.1297 [8] . Study of initial condition recovery from multi-coupled map lattices. Acta Physica Sinica, 2007, 56(12): 6836-6842. doi: 10.7498/aps.56.6836 [9] Jiang Pin-Qun, Wang Bing-Hong, Xia Qing-Hua, Bu Shou-Liang. Control of spatio-temporal chaos in coupled map lattices by state feedback. Acta Physica Sinica, 2004, 53(10): 3280-3286. doi: 10.7498/aps.53.3280 [10] Chen Zheng, Zeng Yi-Cheng, Fu Zhi-Jian. A novel parameter estimation method of signal in chaotic background. Acta Physica Sinica, 2008, 57(1): 46-50. doi: 10.7498/aps.57.46 [11] Cao Xiao-Qun, Song Jun-Qiang, Zhang Wei-Min, Zhao Jun, Zhang Li-Lun. Estimating parameters of chaotic system with variational method. Acta Physica Sinica, 2011, 60(7): 070511. doi: 10.7498/aps.60.070511 [12] Long Wen, Jiao Jian-Jun. Parameter estimation for chaotic system based on evolution algorithm with hybrid crossover. Acta Physica Sinica, 2012, 61(11): 110507. doi: 10.7498/aps.61.110507 [13] Lin Jian, Xu Li. Parameter estimation for chaotic systems based on hybrid biogeography-based optimization. Acta Physica Sinica, 2013, 62(3): 030505. doi: 10.7498/aps.62.030505 [14] Tan Hong-Fang, Jin Tao, Qu Shi-Xian. Frozen random patterns in a globally coupled discontinuous map lattices system. Acta Physica Sinica, 2012, 61(4): 040507. doi: 10.7498/aps.61.040507 [15] Jia Fei-Lei, Xu Wei, Du Lin. Generalized synchronization of different orders of chaotic systems with unknown parameters and parameter identification. Acta Physica Sinica, 2007, 56(10): 5640-5647. doi: 10.7498/aps.56.5640 [16] Wang Liu, He Wen-Ping, Wan Shi-Quan, Liao Le-Jian, He Tao. Evolutionary modeling for parameter estimation for chaotic system. Acta Physica Sinica, 2014, 63(1): 019203. doi: 10.7498/aps.63.019203 [17] Gao Fei, Tong Heng-Qing. Parameter estimation for chaotic system based on particle swarm optimization. Acta Physica Sinica, 2006, 55(2): 577-582. doi: 10.7498/aps.55.577 [18] Li Li-Xiang, Peng Hai-Peng, Yang Yi-Xian, Wang Xiang-Dong. Parameter estimation for Lorenz chaotic systems based on chaotic ant swarm algorithm. Acta Physica Sinica, 2007, 56(1): 51-55. doi: 10.7498/aps.56.51 [19] Wang Shi-Yuan, Feng Jiu-Chao. A novel method of estimating parameter and its application to blind separation of chaotic signals. Acta Physica Sinica, 2012, 61(17): 170508. doi: 10.7498/aps.61.170508 [20] Cao Xiao-Qun. Parameter estimation of nonlinear map based on second-order discrete variational method. Acta Physica Sinica, 2013, 62(8): 080506. doi: 10.7498/aps.62.080506
•  Citation:
##### Metrics
• Abstract views:  3893
• Cited By: 0
##### Publishing process
• Received Date:  19 July 2010
• Accepted Date:  19 October 2010
• Published Online:  15 July 2011

## Parameter estimate from coupled map lattices based on symbolic vector dynamics

• 1. Department of Radio Engineering, Southeast University, Key Laboratory of Underwater Acoustic Signal Processing of Ministry of Education, Southeast University,Nanjing 210096, China

Abstract: 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.

Reference (14)

/