Electronic excitations in molecules can acquire nonlinearity in their transport as a result of strong interactions with vibrations, and stochasticity as a result of thermal fluctuations. The interplay of the nonlinearity and the stochasticity has the potential of producing dramatic effects in the behaviour of the excitations. Such effects, which involve thermally induced limit cycles and Hopf bifurcations, are presented in the specific context of fluorescence depolarization on the basis of a recent generalization of the discrete nonlinear Schroedinger equation.