Dynamical synapses causing self-organized criticality in neural networks

Self-organized criticality1 is one of the key concepts to describe the emergence of complexity in natural systems. The concept asserts that a system self-organizes into a critical state where system observables are distributed according to a power law. Prominent examples of self-organized critical dynamics include piling of granular media2, plate tectonics3 and stick–slip motion4. Critical behaviour has been shown to bring about optimal computational capabilities5, optimal transmission6, storage of information7 and sensitivity to sensory stimuli8,9,10. In neuronal systems, the existence of critical avalanches was predicted11 and later observed experimentally6,12,13. However, whereas in the experiments generic critical avalanches were found, in the model of ref. 11 they only show up if the set of parameters is fine-tuned externally to a critical transition state. Here, we demonstrate analytically and numerically that by assuming (biologically more realistic) dynamical synapses14 in a spiking neural network, the neuronal avalanches turn from an exceptional phenomenon into a typical and robust self-organized critical behaviour, if the total resources of neurotransmitter are sufficiently large.