Back in the saddle again: a computer assisted study of the Kuramoto-Sivashinsky equation
SIAM Journal on Applied Mathematics
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Geometric methods for computing invariant manifolds
Applied Numerical Mathematics - Special issue on numerical methods for ordinary differential equations
Computation and Parametrisation of Invariant Curves and Tori
SIAM Journal on Numerical Analysis
Elements of applied bifurcation theory (2nd ed.)
Elements of applied bifurcation theory (2nd ed.)
Computing Connecting Orbits via an Improved Algorithm for Continuing Invariant Subspaces
SIAM Journal on Scientific Computing
Floquet Theory as a Computational Tool
SIAM Journal on Numerical Analysis
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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.