Binary time series generated by chaotic logistic maps
AbstractThis 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 discretised 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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Bibliographic InfoPaper provided by School of Economics and Finance, Queensland University of Technology in its series School of Economics and Finance Discussion Papers and Working Papers Series with number 208j.
Date of creation: 15 Jun 2006
Date of revision:
Binary sequence; chaos; chaos communications; dependence; discretisation; invariant distribution; logistic map; randomness;
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