On the computation of characteristic multipliers for predicting limit cycle bifurcations
The authors consider local bifurcations of limit cycles in nonlinear dynamical systems. They develop a simple technique to estimate the characteristic multipliers of a limit cycle, using a first-order harmonic balance approximation to the periodic solution under study. This technique analyzes the loss of stability of the limit cycle and gives effective conditions for the prediction of the cyclic fold, flip and Neimark-Sacker bifurcation phenomena; in particular efficient results are given for third-order systems. Several examples are presented.
scientific article; zbMATH DE number 1392785