High-dimensional interior crisis in the Kuramoto-Sivashinsky equation

An investigation of interior crisis of high dimensions in an extended spatiotemporal system exemplified by the Kuramoto-Sivashinsky equation is reported. It is shown that unstable periodic orbits and their associated invariant manifolds in the Poincaré hyperplane can effectively characterize the global bifurcation dynamics of high-dimensional systems.A. C.-L. Chian, E. L. Rempel, E. E. Macau, R. R. Rosa, and F. Christianse