Asymptotic Behavior, Bifurcation and Waves in Reaction-Diffusion Systems and Neuroscience Context (Part I, II)
In this first talk, I will introduce a toy nonlinear model which can be seen as
a toy model for the FitzHugh-Nagumo (FHN) Reaction-Diffusion (RD) Model
well known in Mathematical Neuroscience. I will provide a comprehensive
analysis of the linearized system as well as global convergence results
toward particular solutions for the nonlinear system. The talk will end with
numerical illustrations of solutions.
In this second talk, I will replace the toy model of part I in its context and
point out arising general questions: I will connect the toy model with the
FHN model. I will recall the origin of FHN and its relevance in Neuroscience
context. I will provide theoretical results obtained recently for
nonhomogeneous FHN and exhibit numerical solutions. I will conclude by
listing some questions linked with the two talks.