Statistical independence in nonlinear maps coupled to non-invertible transformations

Kai Wang; Wenjiang Pei; Haishan Xia; Monica Garcia Nustes; J. A. Gonzalez

doi:10.1016/j.physleta.2008.08.054

Statistical independence in nonlinear maps coupled to non-invertible transformations

Kai Wang, Wenjiang Pei, Haishan Xia, Monica Garcia Nustes, J. A. Gonzalez

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We investigate the connections between functions of type x_n = p (θ T zⁿ) and nonlinear maps coupled to non-invertible transformations. These systems can produce unpredictable dynamics. We study the higher-order correlations in the generated sequences. We show that (theoretically) it is possible to construct systems that can generate sequences that constitute a set of statistically independent random variables. We apply the results in the improvement of a two-dimensional coupled map system that has been used in practical applications as e.g. cryptosystems and data compression.

Original language	English
Pages (from-to)	6593-6601
Number of pages	9
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	372
Issue number	44
DOIs	https://doi.org/10.1016/j.physleta.2008.08.054
State	Published - 27 Oct 2008
Externally published	Yes

Keywords

Asymptotic deterministic randomness
Lisssajous maps
Statistical independence

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10.1016/j.physleta.2008.08.054

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title = "Statistical independence in nonlinear maps coupled to non-invertible transformations",

abstract = "We investigate the connections between functions of type xn = p (θ T zn) and nonlinear maps coupled to non-invertible transformations. These systems can produce unpredictable dynamics. We study the higher-order correlations in the generated sequences. We show that (theoretically) it is possible to construct systems that can generate sequences that constitute a set of statistically independent random variables. We apply the results in the improvement of a two-dimensional coupled map system that has been used in practical applications as e.g. cryptosystems and data compression.",

keywords = "Asymptotic deterministic randomness, Lisssajous maps, Statistical independence",

author = "Kai Wang and Wenjiang Pei and Haishan Xia and {Garcia Nustes}, Monica and Gonzalez, {J. A.}",

note = "Funding Information: This work was supported by the Natural Science Foundation of China under Grant No. 60672095, the National High-Technology Project of China under Grant 2007AA11Z210, the Doctoral Fund of Ministry of Education of China under Grant 20070286004, the Special Scientific Foundation for the “Eleventh-Five-Year” Plan of China, and the Excellent Young Teachers Program of Southeast University.",

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T1 - Statistical independence in nonlinear maps coupled to non-invertible transformations

AU - Wang, Kai

AU - Pei, Wenjiang

AU - Xia, Haishan

AU - Garcia Nustes, Monica

AU - Gonzalez, J. A.

N1 - Funding Information: This work was supported by the Natural Science Foundation of China under Grant No. 60672095, the National High-Technology Project of China under Grant 2007AA11Z210, the Doctoral Fund of Ministry of Education of China under Grant 20070286004, the Special Scientific Foundation for the “Eleventh-Five-Year” Plan of China, and the Excellent Young Teachers Program of Southeast University.

PY - 2008/10/27

Y1 - 2008/10/27

N2 - We investigate the connections between functions of type xn = p (θ T zn) and nonlinear maps coupled to non-invertible transformations. These systems can produce unpredictable dynamics. We study the higher-order correlations in the generated sequences. We show that (theoretically) it is possible to construct systems that can generate sequences that constitute a set of statistically independent random variables. We apply the results in the improvement of a two-dimensional coupled map system that has been used in practical applications as e.g. cryptosystems and data compression.

AB - We investigate the connections between functions of type xn = p (θ T zn) and nonlinear maps coupled to non-invertible transformations. These systems can produce unpredictable dynamics. We study the higher-order correlations in the generated sequences. We show that (theoretically) it is possible to construct systems that can generate sequences that constitute a set of statistically independent random variables. We apply the results in the improvement of a two-dimensional coupled map system that has been used in practical applications as e.g. cryptosystems and data compression.

KW - Asymptotic deterministic randomness

KW - Lisssajous maps

KW - Statistical independence

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JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 44

ER -

Statistical independence in nonlinear maps coupled to non-invertible transformations

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Keywords

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