A multiple time renewal equation for neural assemblies with elapsed time model

We introduce and study an extension of the classical elapsed time equation in context neuron populations that are described by since last discharge, i.e., refractory period. In this we incorporate penultimate discharge obtain a more complex system integro-differential equations. For new prove convergence to stationary state means Doeblin's theory case weak non-linearities appropriate functional setting, inspired equation. Moreover, present some numerical simulations observe how different firing rates can give types behaviors contrast them with theoretical results both extended models.