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arXiv · 1310.5233

Showcase of Blue Sky Catastrophes

Leonid Shilnikov·Andrey Shilnikov·Dmitry Turaev
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Abstract

Let a system of differential equations possess a saddle-node periodic orbit such that every orbit in its unstable manifold is homoclinic, i.e. the unstable manifold is a subset of the (global) stable manifold. We study several bifurcation cases where the splitting of such a homoclinic connection causes the Blue Sky Catastrophe, including the onset of complex dynamics. The birth of an invariant torus or a Klein bottle is also described.

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Leonid Shilnikov, Andrey Shilnikov, Dmitry Turaev. 2013-10-19. Showcase of Blue Sky Catastrophes. https://doi.org/10.1142/s0218127414400033

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