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Abstract

We analytically describe a transition scenario to self-organized criticality (SOC) that is new for physics as well as neuroscience; it combines the criticality of first and second-order phase transitions with a SOC phase. We consider a network of pulse-coupled neurons interacting via dynamical synapses, which exhibit depression and facilitation as found in experiments. We analytically show the coexistence of a SOC phase and a subcritical phase connected by a cusp bifurcation. Switching between the two phases can be triggered by varying the intensity of noisy inputs.