A parametric description of phase transitions is done by using general analytical methods involving the bifurcation (branching) of solutions of nonlinear equations in a closed analytical form. The models include one order parameter in the Landau-type kinetic potential, and have been developed to study the impact of both asymmetry and external field on phase transitions in the presence of an intermediate state [1-2]. General analytical solutions, their stability and the realization of different transition scenarios in the whole parameter plane divided into three and four regions respectively, which admit different number of distinct physically acceptable solutions, are discussed.