Seminario
"Disorder and dynamical complexity in a neuronal network model"
Relatore: Stefano Luccioli Centro Interdipartimentale per lo Studio delle Dinamiche Complesse, Università di Firenze e ISC  CNR, Firenze
Aula Feynman
03 Dicembre 2013 ore 16.30
Abstract

Recordings of neuronal activity "in vivo" (i.e. from the brain cortex) show an irregular behavior both at the single neuron level and at the macroscopic (mean field) level.
Here we consider a neuronal network model with disorder in the parameters describing the single neuron evolution and we analyse the effect on the microscopic/macroscopic dynamical complexity.In particular, we focus on the case of neurons characterized by a distribution of spiking frequencies, i.e. in a setup similar to that of the Kuramoto model, which represents the paradigm for the stydy of synchronization phenomena. We see that, upon increasing the coupling strength, the network exhibits a transition from an asynchronous regime to a nontrivial collective behavior. Relevant differences with the Kuramoto model are stressed:
1) First, the dynamics is not chaotic, it eventually converges to a periodic orbit, and the transient time needed to approach the orbit grows exponentially with the number of neurons (this is an instance of the dynamical regime called “stable chaos”).
2) Moreover, the most striking and interesting feature is that the overall macroscopic neural activity shows irregular, seemingly chaotic, oscillations for very large system size.


