Blue sky catastrophe in singularly perturbed systems
- Shilnikov, Andrey
- Shilnikov, Leonid
- Turaev, Dmitry
2010 Mathematics Subject Classification
- 37G15 34E15 37C27 34C26
- saddle-node, global bifurcations, stability boundaries, slow-fast system, bursting oscillations, spikes, excitability
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.