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A method of recovering the initial vectors of globally coupled map lattices based on symbolic dynamics.

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Title: A method of recovering the initial vectors of globally coupled map lattices based on symbolic dynamics.
Authors: Sun Li-Sha1 lssun@stu.edu.cn, Kang Xiao-Yun1, Zhang Qiong2, Lin Lan-Xin3
Source: Chinese Physics B. Dec2011, Vol. 20 Issue 12, p1-8. 8p.
Subjects: Symbolic dynamics, Coupled map lattices, Algorithms, Estimation theory, Chaos theory, Computer simulation, Mathematical functions, Vector analysis
Abstract: Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices (CMLs). It is proved that not all inverse chaotic mapping functions are satisfied for contraction mapping. It is found that the values in phase space do not always converge on their initial values with respect to sufficient backward iteration of the symbolic vectors in terms of global convergence or divergence (CD). Both CD property and the coupling strength are directly related to the mapping function of the existing CML. Furthermore, the CD properties of Logistic, Bernoulli, and Tent chaotic mapping functions are investigated and compared. Various simulation results and the performances of the initial vector estimation with different signal-tonoise ratios (SNRs) are also provided to confirm the proposed algorithm. Finally, based on the spatiotemporal chaotic characteristics of the CML, the conditions of estimating the initial vectors using symbolic dynamics are discussed. The presented method provides both theoretical and experimental results for better understanding and characterizing the behaviours of spatiotemporal chaotic systems. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices (CMLs). It is proved that not all inverse chaotic mapping functions are satisfied for contraction mapping. It is found that the values in phase space do not always converge on their initial values with respect to sufficient backward iteration of the symbolic vectors in terms of global convergence or divergence (CD). Both CD property and the coupling strength are directly related to the mapping function of the existing CML. Furthermore, the CD properties of Logistic, Bernoulli, and Tent chaotic mapping functions are investigated and compared. Various simulation results and the performances of the initial vector estimation with different signal-tonoise ratios (SNRs) are also provided to confirm the proposed algorithm. Finally, based on the spatiotemporal chaotic characteristics of the CML, the conditions of estimating the initial vectors using symbolic dynamics are discussed. The presented method provides both theoretical and experimental results for better understanding and characterizing the behaviours of spatiotemporal chaotic systems. [ABSTRACT FROM AUTHOR]
ISSN:16741056
DOI:10.1088/1674-1056/20/12/120507