# Spike-timing-dependent plasticity with axonal delay tunes networks of Izhikevich neurons to the edge of synchronization transition with scale-free avalanches

## TL;DR

This study demonstrates that a biologically inspired Izhikevich neuronal network with spike-timing-dependent plasticity and axonal delay operates near a critical synchronization transition, exhibiting scale-free avalanches and oscillations, influenced by delay parameters.

## Contribution

The paper introduces a model showing how STDP and axonal delay tune neural networks to a critical state characterized by scale-invariant avalanches and oscillations, addressing key questions about brain criticality.

## Key findings

- Network operates near a synchronization transition point.
- Critical dynamics include scale-free avalanches and finite-size scaling.
- Axonal delay controls supercritical or subcritical regimes.

## Abstract

Critical brain hypothesis has been intensively studied both in experimental and theoretical neuroscience over the past two decades. However, some important questions still remain: (i) What is the critical point the brain operates at? (ii) What is the regulatory mechanism that brings about and maintains such a critical state? (iii) The critical state is characterized by scale-invariant behavior which is seemingly at odds with definitive brain oscillations? In this work we consider a biologically motivated model of Izhikevich neuronal network with chemical synapses interacting via spike-timingdependent plasticity (STDP) as well as axonal time delay. Under generic and physiologically relevant conditions we show that the system is organized and maintained around a synchronization transition point as opposed to an activity transition point associated with an absorbing state phase transition. However, such a state exhibits experimentally relevant signs of critical dynamics including scale-free avalanches with finite-size scaling as well as branching ratios. While the system displays stochastic oscillations with highly correlated fluctuations, it also displays dominant frequency modes seen as sharp peaks in the power spectrum. The role of STDP as well as time delay is crucial in achieving and maintaining such critical dynamics, while the role of inhibition is not as crucial. In this way we provide definitive answers to all three questions posed above. We also show that one can achieve supercritical or subcritical dynamics if one changes the average time delay associated with axonal conduction.