Non-linear oscillations of DNA base pairs

Non-linear oscillations of the nitrogenous bases of DNA, which form pairs: adenine – thymine or guanine – cytosine, are considered. An approach is used in which this biophysical problem can be reduced to a mechanical problem of the non-linear oscillations of two coupled dissimilar pendulums, which oscillate in a plane orthogonal to the principal axis of the molecule. The dynamics of such a model system are analysed. Singular points are obtained in phase space. The eigenvalues of the Jacobi matrix are calculated. The behaviour of the model system close to the singular points is described. The results are illustrated in the form of graphs of the solutions of the corresponding model equations and graphs of the trajectories of motion in configuration space.