Griffiths phase and long-range correlations in a biologically motivated V1 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 \textit{in vivo} and \textit{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 \textit{excitatory postsynaptic potential} in the cortex suggesting that critical behavior 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.

14 pages, 5 figures, PACS: 05.70.Jk,45.70.Ht,87.19.lt

References in corpus (12)

• Emergent complex neural dynamics
• Dynamical synapses causing self-organized criticality in neural networks
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Griffiths phases and the stretching of criticality in brain networks
• Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
• Self-Organized Criticality model for Brain Plasticity
• Spike Avalanches Exhibit Universal Dynamics across the Sleep-Wake Cycle
• Information-based fitness and the emergence of criticality in living systems
• Quasi-Critical Brain Dynamics on a Non-Equilibrium Widom Line
• The brain: What is critical about it?
• Can dynamical synapses produce true self-organized criticality?
• Information processing occurs via critical avalanches in a model of the primary visual cortex

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