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4 papers
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…
Sequence of pseudoequilibria describes the long-time behavior of the nonlinear noisy leaky integrate-and-fire model with large delay
María 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…
On the asymptotic behavior of the NNLIF neuron model for general connectivity strength
María 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…
An understanding of the physical solutions and the blow-up phenomenon for Nonlinear Noisy Leaky Integrate and Fire neuronal models
María J. Cáceres, Alejandro Ramos-Lora
The Nonlinear Noisy Leaky Integrate and Fire neuronal models are mathematical models that describe the activity of neural networks. These models have been studied at a microscopic…