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A well-suited and applicable methodology is proposed to determine stability of equilibrium points for an induction motor (IM) drive systems. Researches indicate that some equilibrium points will lose stability and undergo Hopf bifurcation for some IM drive systems, numerical results validate the proposed methodology. Then, the center manifold theory is introduced and applied to research stability of limit cycles. The n dimensional center manifold and Hopf bifurcation is realized automatically by a Maple computer program, and numerical results validate that limit cycles are stable.