Showcase of Blue Sky Catastrophes

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.

References in corpus (1)

• Key bifurcations of bursting polyrhythms in 3-cell central pattern generators

Cited by in corpus (4)

• Dynamics and bifurcations in multistable 3-cell neural networks
• Critical homoclinics in a restricted four body problem: numerical continuation and center manifold computations
• Homoclinic dynamics in a spatial restricted four body problem blue skies into Smale horseshoes for vertical Lyapunov families
• Homoclinic dynamics in a restricted four body problem