1208.0696 (Stefano Luccioli et al.)

Collective dynamics in sparse networks    [PDF]

Stefano Luccioli, Simona Olmi, Antonio Politi, Alessandro Torcini

The microscopic and macroscopic dynamics of random networks is investigated in the strong-dilution limit (i.e. for sparse networks). By simulating chaotic maps, Stuart-Landau oscillators, and leaky integrate-and-fire neurons, we show that a finite connectivity (of the order of a few tens) is able to sustain a nontrivial collective dynamics even in the thermodynamic limit. Although the network structure implies a non-additive dynamics, the microscopic evolution is extensive (i.e. the number of active degrees of freedom is proportional to the number of network elements).

View original: http://arxiv.org/abs/1208.0696