By imposing symmetry constraints on basic types of bifurcations, equations that properly reproduce the behaviour of the most important instabilities in magnetically confined plasmas are derived. The predictions of these equations are consistent with the results of Tokamak experiments, indicating excellent prospects for the use of equivariant bifurcation theory to interpret the physics of high temperature laboratory plasmas, to forecast and control their macroscopic behaviour and to process the signals of their diagnostics.