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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]
Copyright of Chinese Physics B is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 70535535
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  Data: A method of recovering the initial vectors of globally coupled map lattices based on symbolic dynamics.
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  Data: <searchLink fieldCode="AR" term="%22Sun+Li-Sha%22">Sun Li-Sha</searchLink><relatesTo>1</relatesTo><i> lssun@stu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Kang+Xiao-Yun%22">Kang Xiao-Yun</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Zhang+Qiong%22">Zhang Qiong</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Lin+Lan-Xin%22">Lin Lan-Xin</searchLink><relatesTo>3</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Chinese+Physics+B%22">Chinese Physics B</searchLink>. Dec2011, Vol. 20 Issue 12, p1-8. 8p.
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  Data: <searchLink fieldCode="DE" term="%22Symbolic+dynamics%22">Symbolic dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Coupled+map+lattices%22">Coupled map lattices</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Estimation+theory%22">Estimation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Chaos+theory%22">Chaos theory</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+functions%22">Mathematical functions</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+analysis%22">Vector analysis</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Chinese Physics B is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1088/1674-1056/20/12/120507
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      – Code: eng
        Text: English
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        PageCount: 8
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    Subjects:
      – SubjectFull: Symbolic dynamics
        Type: general
      – SubjectFull: Coupled map lattices
        Type: general
      – SubjectFull: Algorithms
        Type: general
      – SubjectFull: Estimation theory
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      – SubjectFull: Chaos theory
        Type: general
      – SubjectFull: Computer simulation
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      – SubjectFull: Mathematical functions
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      – SubjectFull: Vector analysis
        Type: general
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      – TitleFull: A method of recovering the initial vectors of globally coupled map lattices based on symbolic dynamics.
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            NameFull: Sun Li-Sha
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            NameFull: Kang Xiao-Yun
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            NameFull: Zhang Qiong
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            NameFull: Lin Lan-Xin
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              M: 12
              Text: Dec2011
              Type: published
              Y: 2011
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