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

TL;DR

This paper introduces a method using Gray codes and symbolic dynamics to estimate control parameters in unimodal maps with variable critical points, enabling parameter inference from symbolic sequences.

Contribution

It presents a novel approach to estimate parameters of unimodal maps by analyzing order pattern PDFs derived from Gray codes, even with variable critical points.

Findings

Gray codes effectively estimate PDFs of order patterns

Parameter values can be inferred from symbolic sequences

Method works with maps having variable critical points

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 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 parameter.