Interacting Systems of Infinite Spiking Neurons with Weights Beyond Uniform Summability} \runtit{Interacting systems of neurons beyond uniform summability

I. Papageorgiou

2023, v.29, Issue 3, 435-456


We consider an infinite system of spiking neurons with a drift and both excitatory and inhibitory connections. We study conditions for non-explosiveness and the uniqueness of the invariant measure. In particular, we examine conditions that allow this infinite interacting system to go beyond the usual interactions of uniformly summable weights. As a result, we extend the Galves-L\"ocherbach model beyond the restrictive uniform summability of the model.

Keywords: brain neuron networks, Pure Jump Markov Processes


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