Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

On the periodic solutions of a class of Duffing differential equations

Pages: 277 - 282, Volume 33, Issue 1, January 2013      doi:10.3934/dcds.2013.33.277

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Jaume Llibre - Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain (email)
Luci Any Roberto - Departamento de Matemática, Ibilce -UNESP, 15054-000 São José do Rio Preto, Brazil (email)

Abstract: In this work we study the periodic solutions, their stability and bifurcation for the class of Duffing differential equation $x''+ \epsilon C x'+ \epsilon^2 A(t) x +b(t) x^3 = \epsilon^3 \Lambda h(t)$, where $C>0$, $\epsilon>0$ and $\Lambda$ are real parameter, $A(t)$, $b(t)$ and $h(t)$ are continuous $T$--periodic functions and $\epsilon$ is sufficiently small. Our results are proved using the averaging method of first order.

Keywords:  Periodic solution, averaging method, Duffing differential equation, bifurcation, stability.
Mathematics Subject Classification:  Primary: 34C23, 34C25, 34C29, 34D20, 34G15.

Received: February 2011;      Revised: December 2011;      Available Online: September 2012.