Non-linear dynamics, chaos and phase transitions in DNA molecule

Abstract

DNA molecule is a complex dynamical system consisting of many atoms having a quasi-one-dimensional structure. In this paper, we first review non-linear Hamiltonian DNA dynamics in the form of several Peyrard-Bishoptype DNA models. Then, we explore Hamiltonian chaos and thermodynamical phase transitions related to Hamiltonian DNA dynamics. These second-order phase transitions are shown to have topological origin, rooted in the geometry of the DNA configuration manifold.