Skip Navigation

Journal of the London Mathematical Society 1979 s2-20(2):293-299; doi:10.1112/jlms/s2-20.2.293
© 1979 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Allwright, D. J.
Right arrow Articles by Mees, A. I.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© Oxford University Press

Lyapunov'S Method Applied to the Hopf Bifurcation

D. J. Allwright and A. I. Mees

Department of Pure Mathematics and Mathematical Statistics 16 Mill Lane, Cambridge CB2 1SB

In principle, it is possible to prove the existence and stability of a stable periodic orbit of a set of differential equations by finding a Lyapunov function for it. However, this is usually only practicable for orbits with a particularly simple form. In this paper we first show how a sufficiently good approximation to an exact Lyapunov function can still be used to prove existence of an orbit, though we are not able to determine local uniqueness or stability by our method. Then we show how to construct such an approximation in the case of the orbit produced by the Hopf bifurcation: our method gives a new derivation of the standard formula for the quantity whose sign determines the direction of bifurcation.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.