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Contents of PMS, Vol. 45, Fasc. 1,
pages 33 - 51
DOI: 10.37190/0208-4147.00219
Published online 30.6.2025
 

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

I. Papageorgiou

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 characterization of the invariant state. In particular, we focus on the Galves–Löcherbach model with interactions beyond the Property of Uniform Summability.

2010 AMS Mathematics Subject Classification: Primary 60K35; Secondary 60G99.

Keywords and phrases: brain neuron networks, Replica Mean Field limit, pure jump Markov processes.

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