Difference in chaos suppression increases with network size, tightness of balance, and near the transition to chaos.

A) Dependence of on network size N. With common input, for large N, but is constant for independent input. Error bars indicate interquartile range around the median. B) Dependence of on ‘tightness of balance’ parameter K, which scales both I0 and J0. Results for large K are the same as in A but for small K, the network is no longer in the balanced regime, and results for common and independent input become similar. Error bars indicate ±2 std. C) Dependence of on gain parameter g for low input frequency f. Close to , an arbitrarily small independent input can suppress chaos; this is not the case with common input. The quasi-static approximation (dotted) and DMFT (dashed) results coincide. Error bars indicate ±2 std. Model parameters: I0 = J0 = 1 in A and C; g = 2, f = 0.2/τ in A and B; , in B; f = 0.01/τ in C, N = 5000 in B and C.