From Hopf to Neimark–Sacker bifurcation: a computational algorithm
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

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