Stability Analysis of Damped Cubic-Quintic Duffing Oscillator

Moses O. Oyesanya, Joshua I. Nwamba

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DOI: 10.4236/wjm.2013.31003                

Abstract

This paper presents a comprehensive stability analysis of the dynamics of the damped cubic-quintic Duffing oscillator. We employ the derivative expansion method to investigate the slightly damped cubic-quintic Duffing oscillator obtaining a uniformly valid solution. We obtain a uniformly valid solution of the un-damped cubic-quintic Duffing oscillator as a special case of our solution. A phase plane analysis of the damped cubic-quintic Duffing oscillator is undertaken showing some chaotic dynamics which sends a signal that the oscillator may be useful as model for prediction of earth- quake occurrence.

Keywords

Duffing Oscillator; Cubic-Quintic; Damping; Forcing; Chaos; Derivative Expansion; Stability

Conflicts of Interest

The authors declare no conflicts of interest.

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