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Type: Journal article
Title: Stability and dynamics of a controlled van der Pol-Duffing oscillator
Author: Ji, J.
Hansen, C.
Citation: Chaos Solitons & Fractals, 2006; 28(2):555-570
Publisher: Pergamon-Elsevier Science Ltd
Issue Date: 2006
ISSN: 0960-0779
Statement of
J. C. Ji and C. H. Hansen
Abstract: The trivial equilibrium of a van der Pol–Duffing oscillator under a linear-plus-nonlinear feedback control may change its stability either via a single or via a double Hopf bifurcation if the time delay involved in the feedback reaches certain values. It is found that the trivial equilibrium may lose its stability via a subcritical or supercritical Hopf bifurcation and regain its stability via a reverse subcritical or supercritical Hopf bifurcation as the time delay increases. A stable limit cycle appears after a supercritical Hopf bifurcation occurs and disappears through a reverse supercritical Hopf bifurcation. The interaction of the weakly periodic excitation and the stable bifurcating solution is investigated for the forced system under primary resonance conditions. It is shown that the forced periodic response may lose its stability via a Neimark–Sacker bifurcation. Analytical results are validated by a comparison with those of direct numerical integration.
RMID: 0020060300
DOI: 10.1016/j.chaos.2005.08.021
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Appears in Collections:Mechanical Engineering publications
Environment Institute publications

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