Fig. 4: Large fluctuations.
From: Sustaining a network by controlling a fraction of nodes
Results for scale-free (SF) networks and Erdős-Rényi (ER) with low degrees which have large fluctuations, and thus demand analysis using Eq. (5) rather than Eq. (8). a The order parameter Θ, Eq. (3), for a forced system with ρ = 0.015 and Δ = 5. The network here is scale-free with N = 104, minimal degree k0 = 15, and exponent γ = 3.5. The symbols are from simulations and the line is from theory, Eq. (5). b For the same network as in (a), the (λ, ρ) phase diagram shows a significantly narrower unsustainable regime compared to ER. The black continuous lines are from Eq. (5), while the dashed lines are from Eq. (8), which captures well ER networks but fails to predict SF. c Results for ER network with κ = 10, which is a smaller degree than in Fig. 3g. Also, here, the theory of Eq. (5) (full line) is better than Eq. (8) (dashed line).
