50 citations · 86 across the 7 of their papers we have counts for
9 papers
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…
Global-in-time classical solutions and qualitative properties for the NNLIF neuron model with synaptic delay
María J. Cáceres, Pierre Roux, Delphine Salort +1
The Nonlinear Noisy Leaky Integrate and Fire (NNLIF) model is widely used to describe the dynamics of neural networks after a diffusive approximation of the mean-field limit of a s…
Towards a realistic NNLIF model: Analysis and numerical solver for excitatory-inhibitory networks with delay and refractory periods
María J. Cáceres, Ricarda Schneider
The Network of Noisy Leaky Integrate and Fire (NNLIF) model describes the behavior of a neural network at mesoscopic level. It is one of the simplest self-contained mean-field mode…
Close-to-equilibrium behaviour of quadratic reaction-diffusion systems with detailed balance
María J. Cáceres, José A. Cañizo
We study general quadratic reaction-diffusion systems with detailed balance, in space dimension . We show that close-to-equilibrium solutions (in an sense) are regu…
Blow-up, steady states and long time behaviour of excitatory-inhibitory nonlinear neuron models
María J. Cáceres, Ricarda Schneider
Excitatory and inhibitory nonlinear noisy leaky integrate and fire models are often used to describe neural networks. Recently, new mathematical results have provided a better unde…
Rate of convergence to self-similarity for the fragmentation equation in L^1 spaces
María J. Cáceres, José A. Cañizo, Stéphane Mischler
In a recent result by the authors (ref. [1]) it was proved that solutions of the self-similar fragmentation equation converge to equilibrium exponentially fast. This was done by sh…
Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations
María J. Cáceres, José A. Cañizo, Stéphane Mischler
We study the asymptotic behavior of linear evolution equations of the type \partial_t g = Dg + Lg - λg, where L is the fragmentation operator, D is a differential operator, and λ i…