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Phase response approaches to neural activity models with distributed delay.

Marius Winkler1,2, Grégory Dumont1, Eckehard Schöll2,3,4

  • 1Group for Neural Theory, LNC INSERM U960, DEC, Ecole Normale Supérieure PSL* University, 24 rue Lhomond, 75005, Paris, France.

Biological Cybernetics
|December 2, 2021
PubMed
Summary
This summary is machine-generated.

We developed a theory for neural oscillator networks with distributed coupling delays, calculating phase response curves for brain dynamics. This framework reveals how delay distributions impact neural synchronization stability.

Keywords:
Coupled oscillatorsDistributed delayPhase response curveWilson–Cowan model

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Area of Science:

  • Computational Neuroscience
  • Theoretical Neuroscience
  • Dynamical Systems

Background:

  • Neural oscillator networks are crucial for understanding brain dynamics.
  • Coupling delays in these networks are often distributed, posing analytical challenges.
  • Previous studies primarily focused on non-delayed or discrete-delay systems.

Purpose of the Study:

  • To develop a theoretical framework for calculating phase response curves (PRCs) in oscillatory systems with distributed delays.
  • To extend the theory of weakly coupled oscillators to handle infinite-dimensional phase spaces induced by distributed delays.
  • To investigate the impact of different delay distributions (Gaussian, log-normal) on neural synchronization.

Main Methods:

  • Developed analytical methods to compute PRCs for distributed-delay induced limit cycles.
  • Determined the scalar product and normalization condition for the linearized adjoint system.
  • Applied the framework to the Wilson-Cowan oscillator model and compared results with direct perturbation methods.

Main Results:

  • Successfully calculated PRCs for distributed delay using Gaussian and log-normal distributions.
  • Validated the adjoint calculation method against direct perturbation, confirming its applicability to distributed delays.
  • Phase interaction functions derived from PRCs identified possible phase-locked states and synchronization scenarios.

Conclusions:

  • The developed theory accurately describes weakly coupled oscillators with distributed delays.
  • The distribution of coupling delays significantly influences the stability of synchronization in neural networks.
  • This framework provides a powerful tool for analyzing complex brain dynamics with realistic delay structures.