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The diverse roles of inhibition in neural circuits and other dynamical networks are receiving renewed interest. Here, it is shown that increasing global inhibitory feedback leads to gradual rounding of first-order transition between dynamical phases, turning it into second-order transition. The effect is initially observed in an electronic model consisting of a bi-dimensional array of neon glow lamps, where global inhibition can be simply introduced through a resistor in series with the supply voltage. The experimental findings are confirmed using both an extended numerical model and a mean-field approximation, then replicated across different models of neural dynamics, namely, the Wilson–Cowan model and a network of leaky integrate-and-fire neurons. Across all these systems, a critical point is always found as a function of a pair of parameters controlling local excitability and global inhibition strength, and a general …