Strong interactions with phonons cause nonlinearity to appear in the e
volution of quasiparticles such as electrons, or electronic and vibrat
ional excitations. Our study of the evolution of such nonlinear quantu
m systems, when they are placed in contact with a thermal reservoir, h
as been found to exhibit rich behavior including a Hopf bifurcation. T
he nature of this bifurcation is studied and experimental manifestatio
ns are indicated.