On the computation of characteristic multipliers for predicting limit cycle bifurcations

Abstract

The paper considers local bifurcations of limit cycles in nonlinear dynamical systems. Embedding harmonic balance results in Floquet theory, an approach for locating the characteristic multipliers is developed. The resulting technique, based on a first order approximation, analyses the loss of stability of the limit cycles and gives effective conditions for the prediction of cyclic fold, flip and Neimark-Sacker bifurcation phenomena. In particular, quite efficient results are given for third order systems in the last case. Applying the above procedure, approximated bifurcation loci in the parameter space are obtained. The accuracy of the method is illustrated comparing such results with those computed by the interactive software package AUTO in several application examples.