Bifurcation in the Duffing equation with independent parameters. I
- 1 January 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 78 (1-2) , 57-65
- https://doi.org/10.1017/s0308210500009793
Abstract
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.Keywords
This publication has 2 references indexed in Scilit:
- The bifurcations of duffing's equation: An application of catastrophe theoryJournal of Sound and Vibration, 1976
- Perturbations with several independent parametersJournal of Mathematical Analysis and Applications, 1975