1. Transition between tonic spiking and bursting in a neuron model via Blue-Sky catastrophe Svetlana Zhuravytska

2. Silence Tonic spiking Bursting

3. The functional role of bursting: Observed in sleep and pathological brain states; Mode for control of rhythmic movements; Improves reliability of memory formation.

4. A model of a heart interneuron from the medicinal leech was used to demonstrate the existence of multistability.

5. Voltage-dependent ionic currents: Fast (I Na ) and persistent (I Nap ) sodium currents, Delayed (I K1 ), persistent (I K2 ) and fast (I KA ) potassium currents, Two low-threshold calcium currents (I CaF, I CaS ), Hyperpolarization-activated current (I h ).

6. Simplified model

7. Slow-fast system

8. α=0.003

9. α=0.002

10. α=-0.0235

14. α=-0.024

16. The blue-sky catastrophe occurs when a small amplitude stable limit cycle disappears and a large-amplitude large-period stable orbit appears out of nowhere (from the blue sky)

17. Slow-fast system

21. The saddle-node bifurcation for the periodic orbits constitutes the first component of the blue-sky catastrophe in slow-fast systems. The unstable manifold becomes homoclinic to the periodic orbit. This is the second component of the blue-sky catastrophe.

22. Conclusion The new mechanism of continuous transition between tonic spiking and bursting regimes (blue-sky catastrophe) in a model of a leech heart interneuron was proposed and described in the article.

23. References Transition between Tonic Spiking and Bursting in a Neuron Model via the Blue-Sky Catastrophe, Andrey Shilnikov and Gennady Cymbalyuk. How a neuron model can demonstrate co-existence of tonic spiking and bursting, Gennady Cymbalyuk, Ronald Calabrese, Andrey Shilnikov. Coexistence of tonic spiking oscillations in a leech neuron model, Gennady Cymbalyuk, Andrey Shilnikov.