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arXiv · 2608.10183

Elephant Reinforced Galves-L\"ocherbach Networks

Ioannis Papageorgiou
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Abstract

We introduce an infinite-dimensional Galves--L\"ocherbach system with bounded Elephant-type reinforced synaptic interactions. The reinforcement mechanism modifies the probabilities of excitatory and inhibitory synaptic updates while keeping their amplitudes uniformly bounded. We prove non-explosion by means of a Lyapunov estimate and establish a conditional Wasserstein contraction for the membrane-potential dynamics when the coupled systems share the same reinforcement profile. Finally, we derive the corresponding replica mean-field equation under the Poisson hypothesis.

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Ioannis Papageorgiou. 2026-08-10. Elephant Reinforced Galves-L\"ocherbach Networks. https://arxiv.org/abs/2608.10183

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