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Guckenheimer, J. and Holmes, P. (1983) Global Bifurcations. In: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, New York, 289-352.
https://doi.org/10.1007/978-1-4612-1140-2_6

has been cited by the following article:

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

  AUTHORS: Everestus Obinwanne Eze, Okorafor Chinenye Goodluck, Ujumadu Rosary Ngozi, Toochukwu Ogbonnia Oko

  KEYWORDS: Single-Well Duffing Oscillator, Melnikov Method, Positive Lyapunov Exponent, Threshold Values, MATCAD Software

  JOURNAL NAME: World Journal of Mechanics, Vol.9 No.4, April 25, 2019

  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.