From Hopf to Neimark-Sacker bifurcation: a computational algorithm

Details From Hopf to Neimark-Sacker bifurcation: a computational algorithm From Hopf to Neimark-Sacker bifurcation: a computational algorithm

2007-11-09

arxiv.org/abs/0711.1505v1

Mathematics

Dynamical Systems

To be published in International Journal of Computing Science and Mathematics Volume 1, No. 4, 2007

Scientific paper

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.

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