Comparison Principles and Asymptotic Behavior of Delayed Age-Structured Neuron Models Cáceres Granados, María Josefa Cañizo Rincón, José Alfredo Torres, Nicolás Age-structured models Delay equations Comparison principles In the context of neuroscience the elapsed-time model is an age-structured equation that describes the behavior of interconnected spiking neurons through the time since the last discharge, with many interesting dynamics depending on the type of interactions between neurons. We investigate the asymptotic behavior of this equation in the case of both discrete and distributed delays that account for the time needed to transmit a nerve impulse from one neuron to the rest of the ensemble. To prove the convergence to the equilibrium, we follow an approach based on comparison principles for Volterra equations involving the total activity, which provides a simpler and more straightforward alternative technique than those in the existing literature on the elapsed-time model. 2025-10-10T08:37:06Z 2025-10-10T08:37:06Z 2025-09-26 journal article Cáceres, M.J., Cañizo, J.A. & Torres, N. Comparison Principles and Asymptotic Behavior of Delayed Age-Structured Neuron Models. Acta Appl Math 199, 10 (2025). https://doi.org/10.1007/s10440-025-00746-6 https://hdl.handle.net/10481/106943 10.1007/s10440-025-00746-6 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Springer