eng Science and Education Publishing American Journal of Numerical Analysis 2328-7292 2014-03-22 2 3 69 75 10.12691/ajna-2-3-1 AJNA2014231 article Nizar Jabli jabli.nizar@yahoo.fr 1 Hedi Khammari 2 Mohamed Faouzi Mimouni 3 Department of Electronics, Higher institute of applied sciences and technology, Sousse, Tunisia Department of computer science, Faculty of computer science, Taief, Saudi Arabia Department of electrical engineering, National engineering school of, Monastir, Tunisia Analytical determination of the bifurcation thresholds is of important interest for practical electrical machine design and analysis control. This paper presents mathematical investigation of the qualitative behavior of indirect filed oriented control induction motor based on bifurcation theory. In this context, steady-state responses analysis of the motor model is discussed and an analytical study of generic bifurcations was made. Particular attention is paid to the codimension two bifurcation namely Fold-Hopf bifurcation. The paper introduces some elementary mechanisms of transit from Fold to Fold-Hopf parameter singularity, to derive some analytical rigorous existence conditions and to develop an algorithm for Fold-Hopf bifurcation detection. Some numerical results of equilibrium properties and bifurcation diagrams are then performed to outline our methodology. http://pubs.sciepub.com/ajna/2/3/1/ajna-2-3-1.pdf IFOC Induction Motor steady-state responses bifurcation Fold Hopf Fold-Hopf