The activating fraction a and optimization of dynamical properties. The number of iterations to convergence of the optimization algorithm, as a function of a. 10-node networks were optimized to robustly reach steady state (A) or oscillate (B-D). Different colors represent different levels of connectedness: from left, the degree is 1 (blue), 2 (cyan), 5 (yellow), or 8 (red). Convergence to dynamics that (A) reach steady state or (B) oscillate with period 2 are most rapid for high or low a, respectively. Optimization for period-8 (C) and period-16 (D) oscillation converges most rapidly for intermediate a.