Abstract: By using coefficient of curvature of HOPF bifurcation theorem, in time domain is derived, and the local type of two- dimension system of the theorem to judge the oscillat ion, a new method of analyzing the oscillation of electronic circuits is provided. But the new means of analyzing have to include value comput ing. This article uses the arithmetic of the HOPF bifurcat ion theorem by using graph.A series of graphes can avoid a great deal of comput ing, easily settle the
question of the oscillat ion of nonlinear circuit and provide another means of analyzing the oscillat ion of electronic circuits.

Key words: locus, frequency domain, Niquist criterion, the algorithm of the HOPF bifurcation theorem by using graph