Finding all modes of nonlinear oscillations by the Krawczyk-Moore-Jones algorithm

This paper presents the effective application of Moore and Jones´s algorithm based on Krawczyk operator (KMJ-algorithm) to seeking all the modes of nonlinear oscillations. To show the effectiveness, we take the problem of finding all modes of subharmonic oscillations in three-phase circuits. This problem has not long been resolved because all solutions of the determining equations of amplitudes and phases have not been guaranteed by such conventional numerical method as Newton method. Here in order to apply the KMJ algorithm the determining equations are symbolically derived by extending the asymptotic method. In all the processes of derivation the software Maple is used. The computational results are shown on the parameter space together with the number of solutions.