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Bifurcation in the Duffing equation with independent parameters, II*

Published online by Cambridge University Press:  14 November 2011

Jack K. Hale  and
Hildebrando M. Rodrigues
Jack K. Hale
Affiliation:
Division of Applied Mathematics, Brown University, Providence, R.I., U.S.A. and Department of Mathematics, Heriot-Watt University, Edinburgh
Hildebrando M. Rodrigues
Affiliation:
Division of Applied Mathematics, Brown University, Providence, R.I., U.S.A. and Institute de Ciencias Matematicas de São Carlos, U.S.P., Brasil
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Synopsis

In a previous paper, the authors gave a complete description of the number of even harmonic solutions of Duffing's equation without damping for the parameters varying in a full neighbourhood of the origin in the parameter space. In this paper, the analysis is extended to the case of an independent small damping term. It is also shown that all solutions of the undamped equation are even functions of time.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 79 , Issue 3-4 , 1978 , pp. 317 - 326
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1Chow, S., Hale, J. K. and Mallet-Paret, J.Applications of generic bifurcation II. Arch. Rational Mech. Anal. 62 (1976), 209–236.CrossRefGoogle Scholar
2Hale, J. K. and Rodrigues, H. M.Bifurcation in the Duffing equation with independent parameters I. Proc. Roy. Soc. Edinburgh Sect. A, 78 (1977), 57–65.CrossRefGoogle Scholar
3List, S. Generic bifurcation with application to the von Karman equations. (Providence: Brown Univ. Ph.D. Thesis, 1976).Google Scholar
4Hale, J. K. and Taboas, P. Z. Interaction of damping and forcing in a second order equation. J. Nonlinear Analysis-Theory, Methods, Applications, To appear.Google Scholar