The Berk-Breizman augmentation of the Vlasov-Maxwell system is widely used to model self- consistent resonant excitation and damping of wave fields by evolving energetic particle populations in magnetic fusion plasmas. It is shown here that frequency splitting phenomena displayed by MagnetoHydroDynamic (MHD) oscillations in the Joint European Torus (JET) can be explained by a slow change in time of the Berk-Breizman model parameters. Fully nonlinear self-consistent numerical implementation of this model enables us to construct a rigorous link between the tokamak observations and the classical nonlinear phenomenology of bifurcations, period doubling and the transition to chaos.