A purely mathematical heuristic model is examined in order to explain
the existence of an avoided crossing between two dispersion curves cal
culated for a certain potential energy surface designed to simulate th
e dynamics of a linear polyethylene chain. The model shows that a thir
d mode coupled to a two-mode Fermi-resonant system is able to create a
marked instability in a vibrational spectrum. It is noted that such a
n explanation would require a fourth-order coupling term, which is the
reason given for the failure of normal mode analysis to properly iden
tify this dynamical effect.