From Hopf to Neimark-Sacker bifurcation: a computational algorithm

@misc{citeulike:1902311, 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.}, author = {Moore, Gerald }, citeulike-article-id = {1902311}, eprint = {0711.1505}, keywords = {algorithm, bifurcation, dynamical-system, numeric}, month = {Nov}, posted-at = {2007-11-12 10:28:28}, priority = {2}, title = {From Hopf to Neimark-Sacker bifurcation: a computational algorithm}, url = {http://arxiv.org/abs/0711.1505}, year = {2007} }

TY - ELEC ID - citeulike:1902311 L3 - citeulike-article-id:1902311 TI - From Hopf to Neimark-Sacker bifurcation: a computational algorithm N2 - 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. KW - algorithm KW - bifurcation KW - dynamical-system KW - numeric AU - Moore, Gerald PY - 2007/Nov/09/ UR - http://arxiv.org/abs/0711.1505 ER -