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

Abstract

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 unimodal maps whose dynamics is controlled by an external parameter. Furthermore, these PDFs depend on the value of the external parameter, which 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 parameter.