Simona Olmi - CNR ISC Firenze	#
Collective dynamics 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.