Bifurcation and stability of periodic solutions of Duffing equations

Abstract

We study the stability and exact multiplicity of periodic solutions of the Duffing equation from the global bifurcation point of view and show that the Duffing equation with cubic nonlinearities has at most three T-periodic solutions under a strong damped condition. More precisely, we prove that the T-periodic solutions form a smooth S-shaped curve and the stability of each T-periodic solution is determined by Floquet theory.