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Published March 2013 | Published + Submitted
Journal Article Open

Control of a model of DNA division via parametric resonance


We study the internal resonance, energy transfer, activation mechanism, and control of a model of DNA division via parametric resonance. While the system is robust to noise, this study shows that it is sensitive to specific fine scale modes and frequencies that could be targeted by low intensity electro-magnetic fields for triggering and controlling the division. The DNA model is a chain of pendula in a Morse potential. While the (possibly parametrically excited) system has a large number of degrees of freedom and a large number of intrinsic time scales, global and slow variables can be identified by (1) first reducing its dynamic to two modes exchanging energy between each other and (2) averaging the dynamic of the reduced system with respect to the phase of the fastest mode. Surprisingly, the global and slow dynamic of the system remains Hamiltonian (despite the parametric excitation) and the study of its associated effective potential shows how parametric excitation can turn the unstable open state into a stable one. Numerical experiments support the accuracy of the time-averaged reduced Hamiltonian in capturing the global and slow dynamic of the full system.

Additional Information

© 2013 American Institute of Physics. Received 1 October 2012; accepted 15 January 2013; published online 14 February 2013. This work has been supported by the National Science Foundation under award number NSF-CMMI-092600. We would like to dedicate this paper to the memory of our close collaborator Jerrold E. Marsden. We thank Bryan Eisenhower for giving us the permission to use his figure. W.S.K. thanks Fields Institute for its invitation to the Marsden Conference (July 2012) where he had an opportunity to exchange ideas about this work with other participants.

Attached Files

Published - Chaos_23_013117.pdf

Submitted - 1211.4064.pdf


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August 19, 2023
October 23, 2023