Analysis of the High Order Terms on Periodic Solution Bifurcations of the Generalized Duffing Systems

Abstract

This paper focuses on the effectsof the high order term in Duffing equation. Firstly the averaging equation andthe bifurcation equation are deduced through the multiple scale method.Secondly, the transition sets and several different bifurcation diagrams areobtained based on the singularity theory. The result shows that the high order term induces richer bifurcationcharacteristics.