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Related Experiment Videos

Pulse-coupled resonate-and-fire models.

Keiji Miura1, Masato Okada

  • 1Department of Physics, Graduate School of Sciences, Kyoto University, Kyoto 606-8502, Japan. kmiura@brain.riken.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2004
PubMed
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We analyzed coupled resonate-and-fire neurons and found antiphase states are stable attractors. Our new return map theory analytically explains this stability, revealing unique antiphase states in resonate-and-fire models.

Area of Science:

  • Computational Neuroscience
  • Nonlinear Dynamics
  • Neural Modeling

Background:

  • Neuronal synchronization is crucial for information processing in the brain.
  • Coupled neuron models are essential tools for understanding emergent network dynamics.
  • Resonate-and-fire neuron models capture specific firing behaviors distinct from integrate-and-fire models.

Purpose of the Study:

  • To investigate the existence and stability of antiphase states in pulse-coupled resonate-and-fire neurons.
  • To develop an analytical method for predicting the stability of these antiphase states.
  • To compare the dynamics of resonate-and-fire neurons with integrate-and-fire models.

Main Methods:

  • Numerical simulations of two pulse-coupled resonate-and-fire neurons.

Related Experiment Videos

  • Development and application of a novel return map of firing times for analytical stability analysis.
  • Construction of a phase diagram based on the derived theoretical stability condition.

    • Main Results:

    • Antiphase states were identified as stable attractors in the numerical simulations.
    • The proposed return map method analytically confirmed the stability of antiphase states with a simple condition.
    • The theoretical phase diagram revealed two types of antiphase states, one unique to resonate-and-fire models.

    Conclusions:

    • The analytical theory accurately predicts the behavior observed in numerical simulations of resonate-and-fire neurons.
    • Resonate-and-fire models exhibit unique antiphase dynamics not present in integrate-and-fire models.
    • The developed return map provides a powerful tool for understanding synchronization in neural networks.