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

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

中国物理B ›› 2011, Vol. 20 ›› Issue (12): 120507-120507.doi: 10.1088/1674-1056/20/12/120507

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

孙丽莎¹, 康晓云¹, 林兰馨², 张琼³

(1)College of Engineering, Shantou University, Shantou 515063, China; (2)Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China; (3)Department of Science and Technology, University of Science and Technology of China, Hefei 230026, China

收稿日期:2010-12-29 修回日期:2011-06-23 出版日期:2011-12-15 发布日期:2011-12-15
基金资助:
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).

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

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

^a College of Engineering, Shantou University, Shantou 515063, China; ^b Department of Science and Technology, University of Science and Technology of China, Hefei 230026, China; ^c Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China

Received:2010-12-29 Revised:2011-06-23 Online:2011-12-15 Published:2011-12-15
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: coupled map lattices, symbolic dynamics, initial condition estimation, convergence or divergence property

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.

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

中图分类号: (Synchronization; coupled oscillators)

05.45.Xt

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

孙丽莎, 康晓云, 张琼, 林兰馨. A method of recovering the initial vectors of globally coupled map lattices based on symbolic dynamics[J]. 中国物理B, 2011, 20(12): 120507-120507.

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[J]. Chin. Phys. B, 2011, 20(12): 120507-120507.

参考文献 22

[1]	Wang Y C, Zhao Q C and Wang A B 2008 Chin. Phys. B 17 2373
[2]	Shen M F, Ling L X, Chen J L and and Chang C Q 2010 IEEE Trans. Inst. Meas. 59 1485
[3]	Wang J L and Chen G Z 1999 Acta Phys. Sin. 48 1605 (in Chinese)
[4]	Wang H X and He C 2003 Acta Phys. Sin. 52 2409 (in Chinese)
[5]	Yang W M 1994 Spatiotemporal Chaos and Coupled Map Lattice (Shanghai: Shanghai Scientific and Technological Education Publishing House) p. 13 (in Chinese)
[6]	Kaneko K 1989 Physica D 34 1
[7]	Kaneko K 1990 Physica D 41 137
[8]	Shinbrot T 1994 Phys. Rev. E 50 3230
[9]	Zheng W M and Hao B L 1994 Applied Symbolic Dynamics (Shanghai: Shanghai Scientific and Technological Education Publishing House) p. 50 (in Chinese)
[10]	Xiao F H, Yan G R and Han Y H 2004 Acta Phys. Sin. 53 2877 (in Chinese)
[11]	Hao B L 1994 Starting With Parabolas, An Introduction to Chaotic Dynamics (Shanghai: Shanghai Scientific and Technological Education Publishing House) p. 20 (in Chinese)
[12]	Buminovich L A 1997 Physica D: Nonlinear Pheomena 103 1
[13]	Shawn D P, Ned J C and Erik B 2006 Phys. Rev. Lett. 96 034105
[14]	Zeng Y C and Tong Q Y 2003 Acta Phys. Sin. 52 285 (in Chinese)
[15]	Liu Y, Shen M F and Chen H Y 2006 Acta Phys. Sin. 55 564 (in Chinese)
[16]	Pang Q, Wu W and Fan Y L 2007 Acta Phys. Sin. 56 6836 (in Chinese)
[17]	Wang K, Pei W J, Xia H S and He Z Y 2007 Acta Phys. Sin. 56 3766 (in Chinese)
[18]	Wang K, Pei W J, He Z Y and Cheung Y M 2007 Phys. Lett. A 367 316
[19]	Wang K, Pei W J, Wang S P, Cheung Y M and He Z Y 2008 IEEE Trans. Ciruits Syst. 55 1116
[20]	Shen M F, Liu Y and Lin L X 2009 Chin. Phys. B 18 1761
[21]	Shen M F, Lin L X, Li X Y and Chang C Q 2009 Acta Phys. Sin. 58 2921 (in Chinese)
[22]	Sun L S, Kang X Y and Lin L X 2010 Chin. Phys. B 19 110507

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

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

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 22

相关文章 8

Metrics

本文评价

推荐阅读 0

[1]	董成伟. Topological classification of periodic orbits in Lorenz system[J]. 中国物理B, 2018, 27(8): 80501-080501.
[2]	杨科利, 陈会云, 杜伟伟, 金涛, 屈世显. Partial and complete periodic synchronization in coupled discontinuous map lattices[J]. , 2014, 23(7): 70508-070508.
[3]	丁炯, 张宏, 童勤业, 陈琢. Studies of phase return map and symbolic dynamics in a periodically driven Hodgkin–Huxley neuron[J]. 中国物理B, 2014, 23(2): 20501-020501.
[4]	王福来. A complexity measure approach based on forbidden patterns and correlation degree[J]. 中国物理B, 2010, 19(6): 60515-060515.
[5]	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.
[6]	沈民奋, 刘英, 林兰馨. A method of estimating initial conditions of coupled maplattices based on time-varying symbolic dynamics[J]. 中国物理B, 2009, 18(5): 1761-1768.
[7]	崔迪, 高自友, 赵小梅. Cascades with coupled map lattices in preferential attachment community networks[J]. 中国物理B, 2008, 17(5): 1703-1708.
[8]	肖方红, 郭少华, 胡元太. Evaluating the dynamical coupling between spatiotemporally chaotic signals via an information theory approach[J]. 中国物理B, 2006, 15(7): 1460-1463.