Synaptic delay induced macroscopic dynamics of the large-scale network of Izhikevich neurons
Liang Chen, Sue Ann Campbell

TL;DR
This paper models large-scale neural networks with synaptic delays and adaptation, using mean-field reduction to analyze how delays influence complex collective behaviors like bursting and cross-frequency coupling.
Contribution
It introduces a mean-field model for Izhikevich neurons with synaptic delay and adaptation, analyzing bifurcations and macroscopic dynamics, including novel delay-induced phenomena.
Findings
Synaptic delay can induce new macroscopic oscillations.
Delay influences the emergence of bursting and cross-frequency coupling.
The mean-field model remains valid in the zero heterogeneity limit.
Abstract
We consider a large network of Izhikevich neurons. Each neuron has a quadratic integrate-and-fire type model with a recovery variable modelling spike frequency adaptation (SFA). We introduce a biologically motivated synaptic current expression and a delay in the synaptic transmission. Following the Ott-Antonsen theory, we reduce the network model to a mean-field system of delayed differential equations. Numerical bifurcation analysis allows us to locate higher-codimension bifurcations and to identify the regions in the parameter space where the network exhibits changes in the macroscopic dynamics, including transitions between states where the individual neurons exhibit asynchronous tonic firing and different types of synchronous bursting. We investigate the impact of the heterogeneity of the quenched input current, the SFA mechanism and the synaptic delay on macroscopic dynamics. In…
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Taxonomy
TopicsNeural dynamics and brain function · stochastic dynamics and bifurcation · Nonlinear Dynamics and Pattern Formation
