Устойчивость бегущих волн в модели ДНК Пейрара – Бишопа

Abstract

Traveling waves in the Peyrard — Bishop model (PB model), which describes dynamics of the DNA molecule, are considered. A stability of the traveling waves is investigated in the framework of the long wavelength approximation by using equations in variations and the subsequent use of the method of algebraization by Ince. As a result, the equations in variations are transformed to ones with singular points. To construct boundaries between the regions of stability / instability in space of the system parameters the power series are used. Obtained results are illustrated by numerical simulation using the Runge-Kutta method.