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J. D. Cole and J. Kevorkian, “Uniformly Valid Asymptotic Approximations for Certain Nonlinear Differential Equations,” In: J. P. Laselle and S. Lefschetz, Eds., Nonlinear Differential Equations and Nonlinear Mechanics, Academic, New York, 1963, pp. 113-120. doi:10.1016/B978-0-12-395651-4.50018-0

has been cited by the following article:

• TITLE: Stability Analysis of Damped Cubic-Quintic Duffing Oscillator

  AUTHORS: Moses O. Oyesanya, Joshua I. Nwamba

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

  JOURNAL NAME: World Journal of Mechanics, Vol.3 No.1, February 7, 2013

  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.