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 δ = 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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