Estimation of the control parameter from symbolic sequences: Unimodal maps with variable critical point

Instituto de Fisica Aplicada, Consejo Superior de Investigaciones Cientificas, Serrano 144, 28006 Madrid, Spain.
Chaos (Woodbury, N.Y.) (Impact Factor: 1.95). 07/2009; 19(2):023125. DOI: 10.1063/1.3155072
Source: PubMed


The work described in this paper can be interpreted as an application of the
order patterns of symbolic dynamics when dealing with unimodal maps.
Specifically, it is shown how Gray codes can be used to estimate the
probability distribution functions (PDFs) of the order patterns of parametric
unimodal maps. Furthermore, these PDFs depend on the value of the parameter,
what eventually provides a handle to estimate the parameter value from symbolic
sequences (in form of Gray codes), even when the critical point depends on the

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