Stefano Luccioli - CNR ISC Firenze #
Collective dynamics, extensivity and non-additivity in sparse networks #
The dynamics of sparse networks is investigated both at the microscopic 
and macroscopic level, upon varying the connectivity. In all cases 
(chaotic maps, Stuart-Landau oscillators, and leaky integrate-and-fire 
neuron models), we find that a few tens of random connections are 
sufficient to sustain a nontrivial (and possibly irregular) collective 
dynamics. At the same time, the microscopic evolution turns out to be 
extensive, both in the presence and absence of a macroscopic evolution. 
This result is quite remarkable, considered the non-additivity of the 
underlying dynamical rule.
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Ref: S. Luccioli, S. Olmi, A. Politi and A. Torcini, "Collective dynamics 
in sparse networks", submitted to Phys. Rev. Lett.