Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-29T17:54:48.408Z Has data issue: false hasContentIssue false
  • English
  • Français

The Hopf bifurcation theorem in three dimensions

Published online by Cambridge University Press:  24 October 2008

Peter Swinnerton-Dyer
Peter Swinnerton-Dyer
Affiliation:
St Catharine's College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

The Hopf bifurcation theorem describes the creation of a limit cycle from an isolated singular point of a system of first-order differential equations depending on a parameter. This paper describes a method for determining explicitly a range of values of the parameter throughout which the Hopf configuration continues to exist; only the three-dimensional case is described in this paper, but the method can be generalized.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 3 , November 1977 , pp. 469 - 483
Copyright
Copyright © Cambridge Philosophical Society 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Andronov, A. A., Leontovich, E. A., Gordon, I. I. and Maier, A. G.Qualitative theory of second-order dynamic systems (English translation, John Wiley and Sons, 1973).Google Scholar
(2)Marsden, J. E. and McCracken, M.The Hopf bifurcation and its applications (Springer-Verlag, 1976).CrossRefGoogle Scholar