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arXiv · 1208.0696

Collective dynamics in sparse networks

Stefano Luccioli·Simona Olmi·Antonio Politi·Alessandro Torcini
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Abstract

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).

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Stefano Luccioli, Simona Olmi, Antonio Politi, Alessandro Torcini. 2012-08-03. Collective dynamics in sparse networks. https://doi.org/10.1103/physrevlett.109.138103

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