High-temperature Higgs potential of the two-doublet model in catastrophe theory

We consider the general case of the temperature evolution of the two-doublet Higgs potential of the minimal supersymmetric standard model when vacuum condensates of the Higgs doublets arbitrarily propagate along the equilibrium surface {(}or along the extremum surface{\rm)} passing through bifurcation domains. In the framework of catastrophe theory, the two-doublet Higgs potential of the minimal supersymmetric standard model is a special case of a gradient system potential. We obtain nonlinear transformations of the vacuum condensates of this model, which reduce the two-doublet potential to a canonical form, and catastrophe functions of types $A_3$ and $A_5$ corresponding to an electroweak first-order phase transition in the considered model.