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Dynamical properties of neural networks
Held by Prof. Antonio
Politi (Istituto dei Sistemi Complessi, Firenze, Italy)
In the last two decades most of the studies of high-dimensional dynamical systems were focused on spatio-temporal chaos and delayed systems. More recently, the evolution of networks of oscillators has attracted a large interest for the richness of their behaviour and for the possibility to unveil new information-processing mechanisms.
The literature on this subject is already huge and covers a large variety of phenomena and models. Without pretending to give an exhaustive and unified picture, I'll discuss some general properties of a much studied class of networks, that of pulse-coupled oscillators, with a particular emphasis given to:
(i) the degree of stability of different solutions (in particular, the scaling behaviour with the network size);
(ii) the onset of microscopically irregular but nevertheless stable dynamics;
(iii) the simultaneous occurrence of nontrivial microscopic and macroscopic dynamics.
Finally the relationship with Kuramoto-type of models will be briefly illustrated.