Transition%20between%20tonic%20spiking%20and%20bursting%20in%20a%20neuron%20model%20via%20Blue-Sky%20catastrophe

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Transition between tonic spiking and bursting in
a neuron model via Blue-Sky catastrophe

• Svetlana Zhuravytska

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• Silence
• Tonic spiking
• Bursting

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

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

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• Voltage-dependent ionic currents
• Fast (INa) and persistent (INap) sodium currents,
• Delayed (IK1), persistent (IK2) and fast (IKA)
  potassium currents,
• Two low-threshold calcium currents (ICaF , ICaS),
• Hyperpolarization-activated current (Ih).

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Simplified model
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Slow-fast system
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a0.002
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a-0.0235
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a-0.0235
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a-0.0235
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a-0.0235
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a-0.024
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a-0.024
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• 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)

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Slow-fast system
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• 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.

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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.

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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.