Systèmes complexes et réseaux d'interaction. Application au comportement asymptotique de réseaux de systèmes de réaction-diffusion en neuroscience et en écosystèmes

par Prof. Aziz-Aloui (Université du Havre, LMAH, ISCN, FR-CNRS-3335, France)

mardi 17 déc. 2019, 14:00 → 15:00 Europe/Paris

Neuroscience consists of the study of the nervous system and especially the brain.
The neuron is an electrically excitable cell processing and
transmitting information by electrical and chemical signaling, the
latter via synapses, specialized connections with other cells.
A. L. Hodgkin and A. Huxley proposed the first neuron
model to explain the ionic mechanisms underlying the initiation and
propagation of action potentials in the squid giant axon. Here, we
are interested in the asymptotic behavior of complex networks of
reaction-diffusion (PDE) systems of such neuron models. We show the
existence of the global attractor and the identical synchronization
for the network. We determine analytically, for a given network
topology, the onset of such a synchronization. We then present
numerical simulations and heuristic laws giving the minimum coupling
strength necessary to obtain the synchronization, with respect to the
number of nodes and the network topology.