Replica Mean Field limits for neural networks with excitatory and inhibitory activity

2024/01/19 by Ioannis Papageorgiou, Papageorgiou, Ioannis
Computer Science · Mathematics · Neuroscience · #FOS: Mathematics #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Probability (math.PR) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2401.10955

openalex publication_date 2024/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Replica Mean Field limits for a neural system of infinitely many neurons with both inhibitory and excitatory interactions. As a result we obtain an analytical characterisation of the invariant state. In particular we focus on the Galves-Löcherbach model with interactions beyond the Uniform Summability Principle.

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