Criticality in neural systems is controlled: a mean-field analysis of excitation-inhibition balance

Abstract

Abstract

Abstract The hypothesis that the brain operates at criticality has been widely supported by the observation of neuronal avalanches with approximate power-law distributions in cortical tissue. However, the identification of the corresponding control parameters remains unclear, and the notion of self-organized criticality is often invoked to bypass this problem. Here, we address a complementary notion of criticality, namely a continuous symmetry-breaking transition of the global order parameter, rather than the scaling statistics of neuronal avalanches. We analyze a noisy McCulloch--Pitts network within a mean-field approximation and derive an explicit dynamical map for the average activity. For fixed connectivity, the model incorporates two key control parameters: the noise level and the asymmetry of synaptic weights, which can be interpreted as the balance between excitation and inhibition. We show that critical behavior does not occur at a single point but along a critical manifold in parameter space. A finite-size analysis shows that the numerical pseudocritical point converges toward the mean-field prediction as the network size increases. Additional simulations demonstrate that the order--disorder transition persists in small-world and scale-free networks and when Dale's law is imposed, although network topology and correlations among outgoing synaptic signs can substantially shift and broaden the transition. Our results suggest that neural criticality is not a parameter-free property, but can be regulated by physiologically accessible mechanisms. This provides a simple and physically interpretable framework for understanding how experimental manipulations drive neural systems away from criticality and clarifies the role of the excitation--inhibition balance as a control parameter.