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https://hdl.handle.net/2440/28497
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Type: | Conference paper |
Title: | Stability switches of a controlled van der Pol-Duffing oscillator |
Author: | Ji, J. Lim, C.C. Hansen, C. |
Citation: | Proceedings of the Fourth International DCDIS Conference on Engineering Applications and Computational Algorithms, Ontario, Canada, July 27-29 2005: pp.574-577 |
Publisher: | WATAM PRESS |
Publisher Place: | WATAM PRESS, C/O DCDIS JOURNAL, 317 KAREN PLACE, WATERLOO, ONTARIO N2L 6K8, CANADA |
Issue Date: | 2005 |
ISSN: | 1492-8760 |
Conference Name: | DCDIS International Conference on Engineering Applications and Computational Algorithms (4th : 2005 : Guelph, Ontario, Canada) |
Statement of Responsibility: | J. C. Ji and C. H. Hansen |
Abstract: | The trivial equilibrium of a van der Pol-Duffing oscillator under a nonlinear feedback control may change its stability via either a single or a double Hopf bifurcation if the time delay involved in the feedback reaches certain values. The conditions for switches between stability and instability of the zero solution and the occurrence of Hopf bifurcations are established based on the linear stability analysis. For a double Hopf bifurcation, 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 when the time delay is increased. A stable limit cycle appears after a supercritical Hopf bifurcation occurs and disappears through a reverse supercritical Hopf bifurcation. |
DOI: | 10.1016/j.chaos.2005.08.021 |
Appears in Collections: | Aurora harvest 6 Electrical and Electronic Engineering publications Environment Institute publications |
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