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- W1719059117 abstract "This work is devoted to the study of mathematical questions arising from the modeling of biological systems combining analytic and probabilistic tools. In the first part, we are interested in the derivation of the mean-field equations related to some neuronal networks, and in the study of the convergence to the equilibria of the solutions to the limit equations. In Chapter 2, we use the coupling method to prove the chaos propagation for a neuronal network with delays and random architecture. In Chapter 3, we consider a kinetic FitzHugh-Nagumo equation. We analyze the existence of solutions and prove the nonlinear exponential convergence in the weak connectivity regime. In the second part, we study the role of homeoproteins (HPs) on the robustness of boundaries of functional areas. In Chapter 4, we propose a general model for neuronal development. We prove that in the absence of diffusion, the HPs are expressed on irregular areas. But in presence of diffusion, even arbitrarily small, well defined boundaries emerge. In Chapter 5, we consider the general model in the one dimensional case and prove the existence of monotonic stationary solutions defining a unique intersection point for any arbitrarily small diffusion coefficient. Finally, in the third part, we study a subcritical Keller-Segel equation. We show the chaos propagation without any restriction on the force kernel. Eventually, we demonstrate that the propagation of chaos holds in the entropic sense." @default.
- W1719059117 created "2016-06-24" @default.
- W1719059117 creator A5005777256 @default.
- W1719059117 date "2015-06-02" @default.
- W1719059117 modified "2023-09-27" @default.
- W1719059117 title "Mathematical modeling in neuroscience : collective behavior of neuronal networks & the role of local homeoproteins diffusion in morphogenesis" @default.
- W1719059117 hasPublicationYear "2015" @default.
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