Homoclinic solutions in mechanical systems with small dissipation. Application to DNA dynamics.
This paper analyzes the problem of persistence of homoclinic solutions to perturbed systems of second order ODE's. These systems arise from PDE's, when considering solutions in the form of travelling waves. It is shown that homoclinic solutions persist in the presence of dissipation. Dissipation can be balanced by nonautonomous terms of compact support, which are controlled by a single parameter. This result is applied to prove the existence of torsional pulse-like travelling waves propagating along a nonelastic DNA molecule. In this case the energy is added to system by advancing the RNA polymerase.
Kazmierczak
B
B
Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska St. 21, 00-049 Warsaw, Poland. bkazmier@ippt.gov.pl
Lipniacki
T
T
D004247:DNA / Q000737:chemistry* / Q000378:metabolism; D012321:DNA-Directed RNA Polymerases / Q000737:chemistry* / Q000378:metabolism; D013816:Thermodynamics; D014158:Transcription, Genetic
D004247:DNA; D012321:DNA-Directed RNA Polymerases