Transitional Dynamics and Quasi-Periodic Solution Observed in Two Asymmetrical Coupled Oscillators

Abstract

In this paper, we investigate the transitional dynamics and quasi-periodic solution appearing after the Saddle-Node (SN) bifurcation of a periodic solution in an inductor-coupled asymmetrical van der Pol oscillators with hard-type nonlinearity. In particular, we elucidate, by investigating global bifurcation of unstable manifold (UM) of saddles, that transitional dynamics and quasi-periodic solution after the SN bifurcation appear based on different structure of UM.