  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 (i) first reducing its dynamic to two modes exchanging energy
between each other and (ii) 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.
