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Neural Field Equations and Hawkes processes: long-term stability of traveling wave profiles in the neutral case
Eric Lu\c{c}on (IDP), Christophe Poquet (ICJ)
https://arxiv.org/abs/2507.19236

Neural Field Equations and Hawkes processes: long-term stability of traveling wave profiles in the neutral case
We consider the long-time behavior of a population of interacting Hawkes processes on the real line, with spatial extension. The large population behavior of the system is governed by the standard Voltage-based Neural Field Equation (NFE). We prove long-time stability of the system w.r.t. traveling wave solutions for the NFE on a diffusive time scale, in the neutral case, that is when the speed of the traveling wave solution is zero: the position of the traveling wave profile becomes essentiall…