Influence of periodic field with constant and slowly changing frequency on movement of DNA kink

The movement of a kink in homogeneous polynucleotide chains of DNA under the influence of three kinds of external periodic field—with constant, growing, and decreasing frequencies is investigated in the work. Dependences of speed and coordinate of the kink on time have been found with the help of McLaughlin and Scott energy method. Phase trajectories of the kink have been constructed. It has been shown that in the case of external action with constant frequency, the kink aspires to a limit cycle; in the case of an external field with increasing frequency it tends to a stationary state corresponding to a special point of stable focus type; in the case of an external field with decreasing frequency, the kink transfers from one stationary state (unstable focus) to another (stable focus). The obtained results show the possibility of governing the kink movement by slowly changing the frequency.