title: Collective oscillations in disordered neural networks.
abstract: We investigate the onset of collective oscillations in a excitatory pulse-coupled network of leaky integrate-and-fire neurons in the presence of quenched and annealed disorder. We find that the disorder induces a weak form of chaos that is analogous to that arising in the Kuramoto model for a finite number N of oscillators [O. V. Popovych, Phys. Rev. E 71 065201(R) (2005)]. In fact, the maximum Lyapunov exponent turns out to scale to zero for N-->infinity , with an exponent that is different for the two types of disorder. In the thermodynamic limit, the random-network dynamics reduces to that of a fully homogeneous system with a suitably scaled coupling strength. Moreover, we show that the Lyapunov spectrum of the periodically collective state scales to zero as 1/N{2}, analogously to the scaling found for the "splay state."
authors.affiliation: Physics Department, via Sansone, 1-I-50019 Sesto Fiorentino, Italy. simona.olmi@fi.isc.cnr.it
authors.forename: Simona
authors.initials: S
authors.lastname: Olmi
authors.forename: Roberto
authors.initials: R
authors.lastname: Livi
authors.forename: Antonio
authors.initials: A
authors.lastname: Politi
authors.forename: Alessandro
authors.initials: A
authors.lastname: Torcini
mesh_terms: D008959:Models, Neurological; D009415:Nerve Net / Q000166:cytology / Q000502:physiology*; D009474:Neurons / Q000166:cytology; D013816:Thermodynamics