I am doing an undergraduate project on bars and I am trying to derive the bar instability mode given by Mo et al. It says "whether or not a disk is globally stable depends on the global properties of the disk... it is not possible to write down a universal dispersion relation or stability criterion." I am wondering what the formal, physical definition of an instability is. I know it has something to do with potential energies. Could someone provide a general definition of an instability? Links to sources would be appreciate, as I might want to cite a definition.