The figures below show a global bifurcation for the Kuramoto-Sivashinsky equation. The red unstable manifold bursts through a pair of stable manifolds (in blue) upon a slight change of parameter. The yellow manifold is the unstable manifold of the zero solution. 

The last two plots make a whimsical comparison of the red unstable manifold and a Viking ship found in Oseberg, Norway. 

For more details see the article The Oseberg transition: visualization of global bifurcations for the Kuramoto-Sivashinsky equation, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 11 (2001), no. 1, 1-18.- Michael S. Jolly