61 citations · 79 across the 6 of their papers we have counts for
8 papers
Balanced Dynamics in Strongly Coupled Networks
Cristobal Quininao, Jonathan Touboul
Many mathematical models of interacting agents assume that individual interactions scale down in proportion to the network size, ensuring that the combined input received from the…
Clamping and Synchronization in the strongly coupled FitzHugh-Nagumo model
Cristobal Quiñinao, Jonathan D. Touboul
We investigate the dynamics of a limit of interacting FitzHugh-Nagumo neurons in the regime of large interaction coefficients. We consider the dynamics described by a mean-field mo…
Weak and strong connectivity regimes for a general time elapsed neuron network model
Stéphane Mischler, Cristobal Quiñinao, Qilong Weng
For large fully connected neuron networks, we study the dynamics of homogenous assemblies of interacting neurons described by time elapsed models. Under general assumptions on the…
On a kinetic FitzHugh-Nagumo model of neuronal network
Stéphane Mischler, Cristóbal Quiñinao, Jonathan Touboul
We investigate existence and uniqueness of solutions of a McKean-Vlasov evolution PDE representing the macroscopic behaviour of interacting Fitzhugh-Nagumo neurons. This equation i…
A microscopic spiking neuronal network for the age-structured model
Cristóbal Quiñinao
We introduce a microscopic spiking network consistent with the age-structured/renewal equation proposed by Pakdaman, Perthame and Salort. It is a jump process interacting through a…
Competition and boundary formation in heterogeneous media: Application to neuronal differentiation
Benoit Perthame, Cristobal Quiñinao, Jonathan Touboul
We analyze an inhomogeneous system of coupled reaction-diffusion equations representing the dynamics of gene expression during differentiation of nerve cells. The outcome of this d…
Propagation of chaos for a sub-critical Keller-Segel model
David Godinho, Cristobal Quininao
This paper deals with a sub-critical Keller-Segel equation. Starting from the stochastic particle system associated with it, we show well-posedness results and the propagation of c…
Limits and dynamics of randomly connected neuronal networks
Cristobal Quininao, Jonathan Touboul
Networks of the brain are composed of a very large number of neurons connected through a random graph and interacting after random delays that both depend on the anatomical distanc…