Characterization of a high-dimensional interior crisis in a nonlinear reactive-diffusion equation

We report an investigation of interior crisis in extended spatiotemporal systems exemplified by the Kuramoto–Sivashinsky equation. We show that unstable periodic orbits and their associated invariant stable and unstable manifolds in the Poincaré hyperplane can effectively characterize the global bifurcation dynamics of high-dimensional systems. In particular, we introduce a new technique to characterize the high-dimensional homoclinic tangency responsible for an interior crisis using the stable manifolds of a chaotic saddle.