WIAS Preprint No. 841, (2003)

Blue sky catastrophe in singularly perturbed systems



Authors

  • Shilnikov, Andrey
  • Shilnikov, Leonid
  • Turaev, Dmitry

2010 Mathematics Subject Classification

  • 37G15 34E15 37C27 34C26

Keywords

  • saddle-node, global bifurcations, stability boundaries, slow-fast system, bursting oscillations, spikes, excitability

Abstract

We show that the blue sky catastrophe, which creates a stable periodic orbit whose length increases with no bound, is a typical phenomenon for singularly-perturbed (multi-scale) systems with at least two fast variables. Three distinct mechanisms of this bifurcation are described. We argue that it is behind a transition from periodic spiking to periodic bursting oscillations.

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