by Afshin Montakhab & Mahsa Khoshkhouy (Shiraz University, Iran)
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Critical brain hypothesis has been intensively studied both in experimental and theoretical
neuroscience over the past two decades. However, some important issues are still debated: (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-timing-dependent
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 critical 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 possible answers to all three questions posed above. We also show that
one can achieve supercritical or subcritical dynamics if one adjusts the average time
delay associated with axonal conduction.

In this work, we study the effect of time-delayed spike-time-dependent plasticity (STDP) on a network of Izhikevich neurons with chemical synapses. We are particularly interested in finding the synchronization patterns as a function of the average time delay. Interestingly, we find that there is a standard synchronization phase transition as a function of the average time delay, τ.  We start from a complete network and allow plasticity to take its effect on the synaptic weights.  After a transient time, the networks settles into a dynamical state where the distribution of synaptic weights finds a single-mode distribution. We study the indicators of criticality, i.e. avalanche statistics, finite-size scaling, and branching ratio near the synchronization transition and find that they exhibit experimentally relevant features. Crackling noise relation is also verified.

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