Liapunov exponent distributions and maps for multiple parameter logistic equation. Application to DNA and RNA sequences

Abstract

The multiple parameter logistic equation has previously been utilized to determine the global stability of ternary codes, based on the arrangement of different symbols within the code. This approach has been extended to DNA and RNA sequences, proposing a specific application in the context of reading and translation processes involved in DNA replication and RNA-mediated protein codification. To address the complexity of mapping Liapunov exponents in terms of four parameters representing the different nucleotide bases specialized mapping techniques have been developed. These include Liapunov exponent distributions for entire sequences, as well as binary maps that classify nucleotide bases based on their chemical type (purinic or pyrimidinic). Such methodologies provide a framework for examining the structural and functional properties of genetic material. The sequences analyzed encompass a wide range of DNA and RNA types, including those with and without introns, as well as codifying and noncodifying regions. This multifaceted approach offers valuable insights into the dynamic behavior and stability of nucleotide arrangements, contributing to a deeper understanding of the underlying processes that govern genetic replication and protein synthesis.