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Existence of Chaotic Phenomena in a Single-Well Duffing Oscillator under Parametric Excitations

¹ Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria
² Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria
³ Department of Mathematics, Chukwuemeka Odimegwu Ojukwu University, Uli, Nigeria
⁴ Department of Mathematics, Chukwuemeka Odimegwu Ojukwu University, Uli, Nigeria

World Journal of Mechanics·Volume 09 (2019)·Pages 67–80·Published 24 April 2019·DOI10.4236/wjm.2019.94005

Abstract

In this paper, the existence of chaotic behavior in the single-well Duffing Oscillator was examined under parametric excitations using Melnikov method and Lyapunov exponents. The minimum and maximum values were obtained and the dynamical behaviors showed the intersections of manifold which was illustrated using the MATCAD software. This extends some results in the literature. Simulation results indicate that the single-well oscillator is sensitive to sinusoidal signals in high frequency cases and with high damping factor, the amplitude of the oscillator was reduced.

KeywordsSingle-Well Duffing OscillatorMelnikov MethodPositive Lyapunov ExponentThreshold ValuesMATCAD Software

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Existence of Chaotic Phenomena in a Single-Well Duffing Oscillator under Parametric Excitations

Abstract

References (20)