The Oseberg Transition: Visualization of Global bifurcations for the Kuramoto-Sivashinsky equation

We present and discuss certain global bifurcations involving the interaction of one- and two-dimensional invariant manifolds of steady and periodic solutions of the Kuramoto–Sivashinsky equation. Numerical bifurcation calculations, dimensionality reduction using approximate inertial manifolds/forms, as well as approximation and visualization of invariant manifolds are combined in order to characterize what we term the "Oseberg transition".

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