How synaptic function controls critical transitions in spiking neuron networks: insight from a Kuramoto model...

Area of Science:

• Computational Neuroscience
• Complex Systems
• Mathematical Biology

Background:

• Spiking neuron network dynamics are crucial for understanding emergent collective behavior.
• Synaptic interactions, including dynamics and time delays, significantly influence network function.

Purpose of the Study:

• To analyze the collective dynamics of finite-size quadratic integrate-and-fire neuron networks with general synaptic functions.
• To establish analytical conditions for synaptic coupling (attractive/repulsive) and emergent firing patterns.

Main Methods:

• Employing asymptotic analysis to reduce the integrate-and-fire network to the Kuramoto-Sakaguchi model.
• Expressing Kuramoto-Sakaguchi model parameters explicitly through synaptic function characteristics, activation rates, and time delays.

Main Results:

• Identified analytical conditions for attractive and repulsive synaptic coupling based on synaptic activation rates and time delays.
• Revealed alternating stability regions for synchronous and partially synchronous firing patterns.
• Demonstrated accurate prediction of synchronization, cyclops states, and non-stationary regimes by the reduced model.

Conclusions:

• The reduction approach provides a powerful tool for analyzing rhythmogenesis in complex neural networks.
• This framework facilitates rigorous study of networks with synaptic adaptation and plasticity.
• Understanding synaptic dynamics is key to predicting emergent network behaviors.