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Binary time series generated by chaotic logistic maps

By Anthony J. Lawrance and Rodney C. Wolff


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

Topics: 010400 STATISTICS, 080100 ARTIFICIAL INTELLIGENCE AND IMAGE PROCESSING, Binary sequence, chaos, chaos communications, dependence, discretisation, invariant distribution, logistic map, randomness
Publisher: World Scientific Publishing
Year: 2003
DOI identifier: 10.1142/S0219493703000796
OAI identifier: oai:eprints.qut.edu.au:5938

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