Hierarchy of bifurcations in the truncated and forced nonlinear Schrödinger model.

The truncated forced nonlinear Schrödinger (NLS) model is known to mimic well the forced NLS solutions in the regime at which only one linearly unstable mode exists. Using a novel framework in which a hierarchy of bifurcations is constructed, we analyze this truncated model and provide insights regarding its global structure and the type of instabilities which appear in it. In particular, the significant role of the forcing frequency is revealed and it is shown that a parabolic resonance mechanism of instability arises in the relevant parameter regime of this model. Numerical experiments demonstrating the different types of chaotic motion which appear in the model are provided.