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Periodic solutions in next generation neural field models.

Carlo R Laing1, Oleh E Omel'chenko2

  • 1School of Mathematical and Computational Sciences, Massey University, Private Bag 102-904 NSMC, Auckland, New Zealand.

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Summary
This summary is machine-generated.

This study introduces a new neural field model for theta neurons, finding stable periodic solutions by deriving a self-consistency equation. The method is validated numerically and applied to diverse neural network models.

Keywords:
Neural field modelOtt/AntonsenRiccati equationSelf-consistencyTheta neuron

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Area of Science:

  • Computational Neuroscience
  • Theoretical Neuroscience
  • Complex Systems

Background:

  • Neural field models are crucial for understanding large-scale brain activity.
  • Theta neuron models capture essential dynamics of neuronal firing.
  • Analyzing stability and periodic solutions in neural networks is a key challenge.

Purpose of the Study:

  • To introduce a next-generation neural field model for theta neurons on a ring.
  • To derive and analyze stable time-periodic solutions within this model.
  • To demonstrate the broad applicability of the derived analytical technique.

Main Methods:

  • Utilizing a complex-valued Riccati equation to describe local dynamics.
  • Deriving a self-consistency equation for periodic solutions.
  • Performing stability analysis and numerical simulations.
  • Applying the method to networks with delays, two populations, and Winfree oscillators.

Main Results:

  • Identified conditions for stable time-periodic solutions in the theta neuron network.
  • Developed a self-consistency equation that characterizes these periodic solutions.
  • Demonstrated the technique's effectiveness and generality through numerical examples and extensions.

Conclusions:

  • The derived self-consistency equation provides a powerful analytical tool for neural field models.
  • The method successfully predicts and analyzes stable periodic dynamics in complex neural networks.
  • This approach offers a versatile framework for studying diverse neural architectures.