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# Mathematical Modeling in Biology

The aim of our team is to analyze, theoretically or in collaboration with experimentalists, biological systems and processes with an

approach which combines biological mechanisms and mathematical models which involve in particular partial differential equations and

dynamical systems.

Our current work is structured around two main axes :

The first focuses on neurosciences. On the one hand, we aim to understand the mechanisms underlying phenomena of synchronization/desynchronization if neurons discharge, depending on the strength of interconnections between then and the physiology of the neurons that constitute the network. On the other hand, a project consists in the study of learning brain functions.

The second project, in collaboration with the N. Minc's team, aims at understanding why and how, in yeast cells, the domain of polarisation

adapts to the geometry of the cell.

Adaptation and fatigue model for neuron networks and large time asymptotics in a nonlinear fragmentation equation. Journal of Mathematical Neurosciences. 4(14), (2014). | .

On a voltage-conductance kinetic system for integrate and fire neural networks. ArXiv e-prints. (2013). | .

Relaxation and self-sustained oscillations in the time elapsed neuron network model. ArXiv e-prints. (2011). | .

Dynamics of a structured neuron population. Nonlinearity. 23, pp.55 (2010). | .

A 2-adic approach of the human respiratory tree. ArXiv e-prints. (2010). | .

Trace theorems for trees and application to the human lungs. NHM. pp.469-500 (2009). | .

TRANSPORT EQUATIONS WITH UNBOUNDED FORCE FIELDS AND APPLICATION TO THE VLASOV–POISSON EQUATION. Mathematical Models and Methods in Applied Sciences. 19, pp.199-228 (2009). | .