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The critical brain hypothesis receives increasing support from recentexperimental results. It postulates that the brain is at a critical pointbetween an ordered and a chaotic regime, sometimes referred to as the "edge ofchaos." Another central observation of neuroscience is the principle ofexcitation-inhibition balance: Certain brain networks exhibit a remarkablyconstant ratio between excitation and inhibition. When this balance isperturbed, the network shifts away from the critical point, as may for examplehappen during epileptic seizures. However, it is as of yet unclear whatmechanisms balance the neural dynamics towards this excitation-inhibition ratiothat ensures critical brain dynamics. Here we introduce a simple yetbiologically plausible toy model of a self-organized critical neural networkwith a self-organizing excitation to inhibition ratio. The model only requiresa neuron to have local information of its own recent activity and changesconnections between neurons accordingly. We find that the network evolves to astate characterized by avalanche distributions following universal scaling lawstypical of criticality, and to a specific excitation to inhibition ratio. Themodel connects the two questions of brain criticality and of a specificexcitation/inhibition balance observed in the brain to a common origin ormechanism. From the perspective of the statistical mechanics of such networks,the model uses the excitation/inhibition ratio as control parameter of a phasetransition, which enables criticality at arbitrary high connectivities. We findthat network clustering plays a crucial role for this phase transition tooccur.

A toy model for brain criticality: self-organized excitation/inhibition ratio and the role of network clustering