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本文利用Ｈｏｐｆ分歧理论和中心流形理论，揭示了低频振荡中的非线性奇异现象。提出了与常规线性化分析不同的小干扰稳定域的新观点。得到了在临界点附近即使系统全部特征根都具有负实部时，在小扰动下系统特性和状态也可能发生突变的新结论。
In this paper, Hopf bifurcation theory and central manifold theory are used to reveal the nonlinear singularities in low frequency oscillation. A new viewpoint of small interference stable region which is different from the conventional linear analysis is proposed. The new conclusion that the characteristic and state of the system may change abruptly under small perturbations even if all the eigenvalues of the system have negative real part near the critical point is obtained.