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Interacting systems of infinite spiking neurons with weights beyond uniform summability

Ioannis Papageorgiou

Abstract

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-Löcherbach model beyond the restrictive uniform summability of the model.

Interacting systems of infinite spiking neurons with weights beyond uniform summability

Abstract

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-Löcherbach model beyond the restrictive uniform summability of the model.

Paper Structure

This paper contains 4 sections, 4 theorems, 88 equations.

Table of Contents

  1. Introduction
  2. Long-time behaviour
  3. Non-explosiveness
  4. Wasserstein contraction

Key Result

Theorem 2.1

Assume condition (L). If any of the four conditions (A), (B), (C) or (D) holds, then the process is non-explosive.

Theorems & Definitions (7)

  • Theorem 2.1
  • proof
  • Theorem 2.2
  • proof
  • Corollary 2.3
  • Theorem 2.4
  • proof