Analysis of convergence for initial condition estimation of coupled map lattices based on symbolic dynamics

doi:10.1088/1674-1056/19/11/110507

中国物理B ›› 2010, Vol. 19 ›› Issue (11): 110507-110510.doi: 10.1088/1674-1056/19/11/110507

Analysis of convergence for initial condition estimation of coupled map lattices based on symbolic dynamics

孙丽莎¹, 康晓云¹, 林兰馨²

(1)College of Engineering, Shantou University, Shantou 515063, China; (2)Department of Electronic Engineering, City University of Hong Kong, Hong Kong

收稿日期:2009-12-31 修回日期:2010-07-02 出版日期:2010-11-15 发布日期:2010-11-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 60571066, 60271023 and 61072037), and the Natural Science Foundation of Guangdong Province, China (Grant No. 07008126).

Analysis of convergence for initial condition estimation of coupled map lattices based on symbolic dynamics

Sun Li-Sha(孙丽莎)^a), Kang Xiao-Yun(康晓云)^a)^†, and Lin Lan-Xin(林兰馨)^b)

^a College of Engineering, Shantou University, Shantou 515063, China; ^b Department of Electronic Engineering, City University of Hong Kong, Hong Kong

Received:2009-12-31 Revised:2010-07-02 Online:2010-11-15 Published:2010-11-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 60571066, 60271023 and 61072037), and the Natural Science Foundation of Guangdong Province, China (Grant No. 07008126).

摘要/Abstract

摘要： A novel approach to the inverse problem of diffusively coupled map lattices is systematically investigated by utilizing the symbolic vector dynamics. The relationship between the performance of initial condition estimation and the structural feature of dynamical system is proved theoretically. It is found that any point in a spatiotemporal coupled system is not necessary to converge to its initial value with respect to sufficient backward iteration, which is directly relevant to the coupling strength and local mapping function. When the convergence is met, the error bound in estimating the initial condition is proposed in a noiseless environment, which is determined by the dimension of attractors and metric entropy of the system. Simulation results further confirm the theoretic analysis, and prove that the presented method provides the important theory and experimental results for better analysing and characterizing the spatiotemporal complex behaviours in an actual system.

Abstract: A novel approach to the inverse problem of diffusively coupled map lattices is systematically investigated by utilizing the symbolic vector dynamics. The relationship between the performance of initial condition estimation and the structural feature of dynamical system is proved theoretically. It is found that any point in a spatiotemporal coupled system is not necessary to converge to its initial value with respect to sufficient backward iteration, which is directly relevant to the coupling strength and local mapping function. When the convergence is met, the error bound in estimating the initial condition is proposed in a noiseless environment, which is determined by the dimension of attractors and metric entropy of the system. Simulation results further confirm the theoretic analysis, and prove that the presented method provides the important theory and experimental results for better analysing and characterizing the spatiotemporal complex behaviours in an actual system.

Key words: coupled map lattices, convergence, symbolic dynamics, initial condition estimation

中图分类号: (Inverse problems)

02.30.Zz

05.45.Ra (Coupled map lattices) 05.70.Ce (Thermodynamic functions and equations of state)

孙丽莎, 康晓云, 林兰馨. Analysis of convergence for initial condition estimation of coupled map lattices based on symbolic dynamics[J]. 中国物理B, 2010, 19(11): 110507-110510.

Sun Li-Sha(孙丽莎), Kang Xiao-Yun(康晓云), and Lin Lan-Xin(林兰馨). Analysis of convergence for initial condition estimation of coupled map lattices based on symbolic dynamics[J]. Chin. Phys. B, 2010, 19(11): 110507-110510.

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Analysis of convergence for initial condition estimation of coupled map lattices based on symbolic dynamics

Analysis of convergence for initial condition estimation of coupled map lattices based on symbolic dynamics

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