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

doi:10.1088/1674-1056/20/12/120507

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-to-noise 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.

Keywords: coupled map lattices symbolic dynamics initial condition estimation convergence or divergence property

Received: 29 December 2010
Revised: 23 June 2011
Accepted manuscript online:

PACS:	05.45.Xt	(Synchronization; coupled oscillators)
	05.45.-a	(Nonlinear dynamics and chaos)
	07.05.Kf	(Data analysis: algorithms and implementation; data management)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61072037 and 60271023) and the Natural Science Foundation of Guangdong Province, China (Grant No. 10151503101000011).

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Sun Li-Sha(孙丽莎), Kang Xiao-Yun(康晓云), Zhang Qiong(张琼), and Lin Lan-Xin(林兰馨) A method of recovering the initial vectors of globally coupled map lattices based on symbolic dynamics 2011 Chin. Phys. B 20 120507

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

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