From Hopf to Neimark–Sacker bifurcation: a computational algorithm Online publication date: Fri, 25-Jul-2008
by Gerald Moore
International Journal of Computing Science and Mathematics (IJCSM), Vol. 2, No. 1/2, 2008
Abstract: We construct an algorithm for approximating the invariant tori created at a Neimark–Sacker bifurcation point. It is based on the same philosophy as many algorithms for approximating the periodic orbits created at a Hopf bifurcation point, i.e., a Fourier spectral method. For Neimark–Sacker bifurcation, however, we use a simple parametrisation of the tori in order to determine low-order approximations, and then utilise the information contained therein to develop a more general parametrisation suitable for computing higher-order approximations. Different algorithms, applicable to either autonomous or periodically-forced systems of differential equations, are obtained.
Online publication date: Fri, 25-Jul-2008
Go to Inderscience Online Journals to access the Full Text of this article.
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Computing Science and Mathematics (IJCSM):
Login with your Inderscience username and password:
Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.
If you still need assistance, please email email@example.com