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Using Neuron Spiking Activity to Trigger Closed-Loop Stimuli in Neurophysiological Experiments

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Published on: November 12, 2019

Bursting frequency versus phase synchronization in time-delayed neuron networks.

Anders Nordenfelt¹, Javier Used, Miguel A F Sanjuán

¹Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, España.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 18, 2013

Summary

This summary is machine-generated.

We studied how time delays affect neuron network bursting frequency and phase synchronization. Results show these measures often mirror each other, especially in chaotic neuron models and Kuramoto models.

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Area of Science:

Computational Neuroscience
Complex Systems Dynamics
Network Science

Background:

Time delays in neural connections are crucial for network dynamics.
Understanding the relationship between bursting frequency and phase synchronization is key to characterizing neural network behavior.

Purpose of the Study:

To investigate the dependence of average bursting frequency on time delay in neuron networks.
To compare this dependence with phase synchronization in both neuron and Kuramoto models.
To derive analytical relationships between mean frequency and phase synchronization in Kuramoto models.

Main Methods:

Analysis of randomly distributed time-delayed chemical synapses in neuron networks.
Utilizing the chaotic Rulkov model and the continuous Hindmarsh-Rose model.
Employing time-delayed Kuramoto models for analytical insights.

Main Results:

A strong similarity, often appearing as mirror images, was observed between bursting frequency and phase synchronization curves across different intervals.
Both the Rulkov and Hindmarsh-Rose neuron models exhibited this phenomenon.
Analytical formulas derived for Kuramoto models revealed an implicit functional relationship between mean frequency and phase synchronization.

Conclusions:

The observed similarities between bursting frequency and phase synchronization are likely due to a strong underlying functional dependence.
Time delays play a significant role in shaping the collective dynamics of neural networks.
The findings provide a deeper understanding of synchronization phenomena in complex neural systems.