@MASTERSTHESIS\{IMM1998-01024,
    author       = "K. B. Hilger and D. S. Luciani",
    title        = "Forced Oscillators - A Detailed Numerical Bifurcation Analysis",
    year         = "1998",
    month        = "aug",
    school       = "Center for Chaos and Turbulence Studies, Department of Physics, Technical University of Denmark",
    address      = "{DTU,} {DK-}2800 Kgs. Lyngby",
    type         = "",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/1024-full.html",
    abstract     = "A detailed computational study of the dynamics of a forced oscillator is presented. The system examined is a modifed version of the generic normal form for a Hopf bifurcation subjected to an external sinusoidal perturbation. Breaking of the symmetry of the normal form is necessary in order to achieve a coupling between the external forcing and the autonomous oscillations of the system. A parameter is, therefore, introduced enabling the strength of the coupling to be controlled. Parameters controlling the stability and frequency of the oscillations are chosen, so that the system includes two supercritical Hopf bifurcations enclosing a region of autonomous oscillations. Representative tongue structures in the forcing parameter plane are examined and presented. The analyses presented in this work elucidated features common to oscillators forced across a Hopf bifurcation. In addition, the generic model proposed provides a high degree of control of the underlying bifurcations and dynamics of the autonomous system, and thus may provide a foundation for future investigations of forced non-stationary systems."
}