Optimal control of excitable systems near criticality

Abstract

Experiments suggest that the cerebral cortex gains several functional advantages by operating in a dynamical regime near the critical point of a phase transition. However, a long-standing criticism of this hypothesis is that critical dynamics are rather noisy, which might be detrimental to aspects of brain function that require precision. If the cortex does operate near criticality, how might it mitigate the noisy fluctuations? One possibility is that other parts of the brain may act to control the fluctuations and reduce cortical noise. To better understand basic aspects of controlling neural activity fluctuations, here we numerically and analytically study a network of binary neurons. We determine how the efficacy of controlling the population firing rate depends on proximity to criticality as well as different structural properties of the network. We find that control is most effective-errors are minimal for the widest range of target firing rates-near criticality. Optimal control is slightly away from criticality for networks with heterogeneous degree distributions. Thus, while criticality is the noisiest dynamical regime, it is also the regime that is easiest to control, which may offer a way to mitigate the noise.