Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe.

@article{Shilnikov2005TransitionBT,
  title={Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe.},
  author={Andrey Shilnikov and Gennady Cymbalyuk},
  journal={Physical review letters},
  year={2005},
  volume={94 4},
  pages={048101}
}
We study a continuous and reversible transition between periodic tonic spiking and bursting activities in a neuron model. It is described as the blue-sky catastrophe, which is a homoclinic bifurcation of a saddle-node periodic orbit of codimension one. This transition constitutes a biophysically plausible mechanism for the regulation of burst duration that increases with no bound like 1/square root alpha-alpha0 as the transition value alpha0 is approached.