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Bifurcation and stability of periodic solutions of Duffing equations

Hongbin Chen1 and Yi Li2

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Recommended by D Treschev

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.


PACS

05.45.-a Nonlinear dynamics and nonlinear dynamical systems

MSC

37K05 Hamiltonian structures, symmetries, variational principles, conservation laws

37K50 Bifurcation problems

37K45 Stability problems

37K55 Perturbations, KAM for infinite-dimensional systems

Subjects

Statistical physics and nonlinear systems

Dates

Issue 11 (November 2008)

Received 3 December 2007, in final form 2 September 2008

Published 29 September 2008



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