Dynamic behavior of two-phase systems in physical equilibrium

Abstract

The steady state and dynamic behavior of two-phase systems in physical equilibrium is investigated. The autonomous and non-autonomous systems are considered. The pseudo-arclength bifurcation technique reveals steady state multiplicity patterns not previously observed, including isola and mushroom patterns. It is shown that degenerate singular points of codimension 2, which violate the non-singularity and transversality conditions of the classical Hopf theorem exist. The effect of the forcing amplitude and frequency on the behavior of the non-autonomous system is investigated at a number of chosen positions of the center of forcing. It is found that the forced system is very sensitive to the position of the center of forcing relative to Hopf bifurcation points of the unforced system. The excitation diagram shows that a period doubling region may exist at the top of a 2/1 resonance horn. It is shown that a Hopf bifurcation curve of the stroboscopic map is originated at bifurcation points having double −1 Floquet multipliers.