title: Griffiths phase and long-range correlations in a biologically motivated visual cortex model.
abstract: Activity in the brain propagates as waves of firing neurons, namely avalanches. These waves' size and duration distributions have been experimentally shown to display a stable power-law profile, long-range correlations and 1/f (b) power spectrum in vivo and in vitro. We study an avalanching biologically motivated model of mammals visual cortex and find an extended critical-like region - a Griffiths phase - characterized by divergent susceptibility and zero order parameter. This phase lies close to the expected experimental value of the excitatory postsynaptic potential in the cortex suggesting that critical be-havior may be found in the visual system. Avalanches are not perfectly power-law distributed, but it is possible to collapse the distributions and define a cutoff avalanche size that diverges as the network size is increased inside the critical region. The avalanches present long-range correlations and 1/f (b) power spectrum, matching experiments. The phase transition is analytically determined by a mean-field approximation.
authors.affiliation: Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil.
authors.forename: M
authors.initials: M
authors.lastname: Girardi-Schappo
authors.affiliation: Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil.
authors.forename: G S
authors.initials: GS
authors.lastname: Bortolotto
authors.affiliation: Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil.
authors.forename: J J
authors.initials: JJ
authors.lastname: Gonsalves
authors.affiliation: Departamento de Engenharia Química e Engenharia de Alimentos, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil.
authors.forename: L T
authors.initials: LT
authors.lastname: Pinto
authors.affiliation: Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil.
authors.forename: M H R
authors.initials: MH
authors.lastname: Tragtenberg
mesh_terms: D000200:Action Potentials; D000818:Animals; D006801:Humans; D008322:Mammals / Q000502:physiology*; D008959:Models, Neurological; D044367:Phase Transition; D009435:Synaptic Transmission; D014793:Visual Cortex / Q000502:physiology*