title: Collective dynamics in sparse networks.
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 nonadditive dynamics, the microscopic evolution is extensive (i.e., the number of active degrees of freedom is proportional to the number of network elements).
authors.affiliation: CNR-Consiglio Nazionale delle Ricerche-Istituto dei Sistemi Complessi, Sesto Fiorentino, Italy.
authors.forename: Stefano
authors.initials: S
authors.lastname: Luccioli
authors.forename: Simona
authors.initials: S
authors.lastname: Olmi
authors.forename: Antonio
authors.initials: A
authors.lastname: Politi
authors.forename: Alessandro
authors.initials: A
authors.lastname: Torcini
mesh_terms: D008962:Models, Theoretical; D009474:Neurons / Q000166:cytology / Q000502:physiology; D010507:Periodicity