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Intermittency in the Hodgkin-Huxley model.

Gaspar Cano1, Rui Dilão2,3

  • 1Nonlinear Dynamics Group, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, Lisbon, Portugal.

Journal of Computational Neuroscience
|June 16, 2017
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Summary

Action potentials in the Hodgkin-Huxley neuron model arise from type I intermittency near a saddle-node bifurcation. Spatially extended models reveal chaotic intermittency during transitions from turbulent to resting states.

Keywords:
Chaotic intermittencyDiffusion wavesHodgkin-Huxley neuron modelType I intermittency

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Area of Science:

  • Computational neuroscience
  • Nonlinear dynamics
  • Biophysics

Background:

  • The Hodgkin-Huxley model is a cornerstone for understanding neuronal excitability.
  • Neuronal firing patterns can exhibit complex dynamics, including intermittent behavior.

Purpose of the Study:

  • To investigate the underlying mechanisms of action potential generation in the Hodgkin-Huxley model.
  • To analyze the dynamics of action potential propagation in spatially extended neuronal models.
  • To characterize novel intermittent phenomena in neuronal models.

Main Methods:

  • Analysis of the Hodgkin-Huxley neuron model using bifurcation theory.
  • Simulation of the spatially extended Hodgkin-Huxley model for action potential propagation.
  • Identification and characterization of intermittency types and diffusion waves.

Main Results:

  • Action potentials originate from type I intermittency near a saddle-node bifurcation of limit cycles.
  • The spatially extended model exhibits both type I and a novel chaotic intermittency.
  • Regular and chaotic diffusion waves were observed during action potential propagation.
  • Chaotic intermittency involves transitions from turbulent to resting states, marked by irregular spike intervals.

Conclusions:

  • Type I intermittency is a key mechanism for action potential generation in the Hodgkin-Huxley model.
  • Complex intermittent dynamics, including chaotic intermittency, influence neuronal signal propagation.
  • These findings offer new insights into the diverse firing patterns and signal transmission in neurons.