Binary time series generated by chaotic logistic maps

Lawrance, Anthony J. & Wolff, Rodney C. (2003) Binary time series generated by chaotic logistic maps. Stochastics and Dynamics, 3(4), pp. 529-544.

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This paper examines stochastic pairwise dependence structures in binary time series obtained from discretised versions of standard chaotic logistic maps. It is motivated by applications in communications modelling which make use of so-called chaotic binary sequences. The strength of non-linear stochastic dependence of the binary sequences is explored. In contrast to the original chaotic sequence, the binary version is non-chaotic with non-Markovian non-linear dependence, except in a special case. Marginal and joint probability distributions, and autocorrelation functions are elicited. Multivariate binary and more discretized time series from a single realisation of the logistic map are developed from the binary paradigm. Proposals for extension of the methodology to other cases of the general logistic map are developed. Finally, a brief illustration of the place of chaos-based binary processes in chaos communications is given.

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ID Code: 5938
Item Type: Journal Article
Refereed: Yes
Keywords: Binary sequence, chaos, chaos communications, dependence, discretisation, invariant distribution, logistic map, randomness
DOI: 10.1142/S0219493703000796
ISSN: 0219-4937
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > ARTIFICIAL INTELLIGENCE AND IMAGE PROCESSING (080100)
Divisions: Current > QUT Faculties and Divisions > QUT Business School
Copyright Owner: Copyright 2003 World Scientific Publishing
Copyright Statement: Electronic version of an article published as [Stochastics and Dynamics 3(4):pp. 529-544.
] [] © [copyright World Scientific Publishing Company] [Stochastics and Dynamics]
Deposited On: 05 Jan 2007 00:00
Last Modified: 29 Feb 2012 12:59

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