An analytical study of low-codimension bifurcations of indirect field-oriented control of induction motor

Mathematically, bifurcation theory attempts to investigate the changes in the qualitative or topological structure of a studied equation models. Given paper focuses on an analytical investigation of the nonlinear behavior of an indirect filedoriented control of induction motor. In this context, steady-state responses of the motor model are discussed and an analytical study of the generic codimension one bifurcation, Hopf and Fold bifurcations, was made. Of special interest here is the codimension two bifurcation namely a Double Hopf bifurcation. The purpose of this paper is to present some elementary mechanisms of such singularity, to derive some analytical rigorous existence condition and to develop an algorithm for DHbifurcation detection. A numerical investigation of some qualitative properties and bifurcation phenomena is then performed to outline the role of Double-Hopf (DH) and Generalized Hopf (GH) codimension two bifurcations in organizing multistability of limit cycles and local chaos phenomena.