Computing Two-Dimensional Global Invariant Manifolds in Slow-fast Systems

We present the GlobalizeBVP algorithm for the computation of two-dimensional stable and unstable manifolds of a vector field. Specifically, we use the collocation routines of Auto to solve boundary problems that are used during the computation to find the next approximate geodesic level set on the manifold. The resulting implementation is numerically very stable and well suited for systems with multiple time scales. This is illustrated with the test-case example of the well-known Lorenz manifold, and with a slow-fast model of a somatotroph cell.