An application of bifurcation of periodic solutions to ferroresonance over-voltage in power systems (Q1191672)

This paper concerns the solution properties of a four-dimensional ordinary differential equation with a periodic excitation (non autonomous equation). This equation is considered as the model of an electrical power system which can give rise to ferroresonance overvoltage. The authors prove the existence of a two-dimensional integral manifold in the four-dimensional phase space, on which all the solutions are uniformly bounded, and an harmonic solution exists. This solution is asymptotically stable. In the four-dimensional space, solutions and their antisymmetrical ones exist. They merge on the two-dimensional integral manifold. The paper references don't mention the classical results of Hayashi on ferroresonance phenomena. The bifurcations study is very limited and only implicit in section 4. Higher harmonic resonances are not considered. It is the same for subharmonic resonances.