PARAMETRIC REPRESENTATION AND BIFURCATION ANALYSIS OF THE CUBIC EQUATION SOLUTIONS WITH APPLICATION TO THE PHASE TRANSITIONS

Alexandr A. BARSUK, Florentin PALADI Moldova State University

Abstract

Real solutions representation for the cubic equation with real coefficients in a parametric form is given. The dependence of the solutions on the equation coefficients and the bifurcation conditions for these solutions are studied. In the parametric space regions with one and three real solutions are considered. Using parametric representations of the cubic equation solutions, the stability and bifurcation conditions of the equilibrium states for the thermodynamic systems described by the Landau-type kinetic potential are analyzed. Keywords: phase transitions, metastable state, bifurcation analysis.