Investigating Duffing Oscillator using Bifurcation Diagrams

Abstract

This paper investigates the dynamical behaviour of a duffing oscillator using

bifurcation diagrams. There has been growing interest and challenges in

engineering dynamics to characterize dynamical systems that are chaotic using

bifurcation diagrams. The relevant second order differential equations using

Runge-Kutta method were solved for ranges of appropriate parameters. The

solutions obtained were used to produce the bifurcation diagrams using

Microsoft excel 2007. Since an average estimate of 5 = 4.668 from the

bifurcation diagrams produced is an approximate value of the Feigenbaum

.constant as widely reported in the literatures, it can be deduced that the

bifurcation diagrams conforms to the expected results. While the bifurcation

diagrams revealed the dynamics of the duffing oscillator, it also shows that the

dynamics depend strongly on the initial conditions.

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