3 papers
math.AP2024
Sequence of pseudoequilibria describes the long-time behavior of the nonlinear noisy leaky integrate-and-fire model with large delay
MarÃa J. Cáceres, José A. Cañizo, Alejandro Ramos-Lora
There is a wide range of mathematical models that describe populations of large numbers of neurons. In this article, we focus on nonlinear noisy leaky integrate-and-fire (NNLIF) mo…
math.NA2024
Discrete minimizers of the interaction energy in collective behavior: a brief numerical and analytic review
José A. Cañizo, Alejandro Ramos-Lora
We consider minimizers of the N-particle interaction potential energy and briefly review numerical methods used to calculate them. We consider simple pair potentials which are repu…
math.AP2024
On the asymptotic behavior of the NNLIF neuron model for general connectivity strength
MarÃa J. Cáceres, José A. Cañizo, Alejandro Ramos-Lora
We prove new results on the asymptotic behavior of the nonlinear integrate-and-fire neuron model. Among them, we give a criterion for the linearized stability or instability of equ…