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Bifurcation in the Duffing equation with independent parameters. I

Published online by Cambridge University Press:  14 February 2012

Jack K. Hale  and
Hildebrando M. Rodriques
Jack K. Hale
Affiliation:
Lefschetz Center for Dynamical Systems, Division of Applied Mathematics Brown University, Providence, R.I., USA
Hildebrando M. Rodriques
Affiliation:
Lefschetz Center for Dynamical Systems, Division of Applied Mathematics Brown University, Providence, R.I., USA
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Synopsis

In the standard treatment of the harmonic solutions of Duffing's equation with small non-linearities and small forcing, all small parameters are assumed to be common multiples of some small parameter. As a consequence, the parameters do not vary in a full neighbourhood of zero and the bifurcation surfaces are not obtained. It is the purpose of this paper to give a complete description of the number of harmonic solutions for the parameters varying in a full neighbourhood of the origin in the parameter space.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 78 , Issue 1-2 , 1977 , pp. 57 - 65
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

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