Feigenbaum Cascade of Discrete Breathers in a Model of DNA

TL;DR

This paper reveals a cascade of discrete breathers in a DNA model, showing their emergence from stability overlaps in driven nonlinear oscillators, with potential implications for gene expression.

Contribution

It introduces the existence of a Feigenbaum cascade of discrete breathers in a DNA model, linking nonlinear dynamics to biological processes.

Findings

Discrete breathers appear from the anti-continuum limit.

A cascade of breathers exists due to stability overlaps.

Potential impact on understanding gene expression.

Abstract

We demonstrate that period-doubled discrete breathers appear from the anti-continuum limit of the driven Peyrard-Bishop-Dauxois model of DNA. These novel breathers result from a stability overlap between sub-harmonic solutions of the driven Morse oscillator. Sub-harmonic breathers exist whenever a stability overlap is present within the Feigenbaum cascade to chaos and therefore an entire cascade of such breathers exists. This phenomenon is present in any driven lattice where the on-site potential admits sub-harmonic solutions. In DNA these breathers may have ramifications for cellular gene expression.