Fig. 5: Benefit of non-Markovian recovery to making the network more resilient against large-scale failures.
From: Non-Markovian recovery makes complex networks more resilient against large-scale failures
Shown are results from the NMR model through simulations, PA analysis, and mean-field theory. a Time evolution of inactive nodes from the initial conditions [X]0 = [Y]0 = 0, for β1 = 0.009, β2 = 2.0, τ1 = 100 (thus μ1 = 0.01), and τ2 = 1.0 (thus μ2 = 1.0). A number of time instants are marked for better visualization of the time evolution in different stages: tO = 0, tA = 43.51, tB = 64.68, tC = 100, tD = 164.51, and tE = 480. b Phase diagram in the (β2 − β1) parameter plane for τ1 = 100 and τ2 = 1.0. The symbols are numerical results, and the solid and dashed curves are obtained from the PA analysis and mean-field theory, respectively. c Dependence of βc for reaching a high-failure state on the initial value of [X]0 with [Y]0 = 0. The error bars with the simulation results are about 6 × 10−5, which are obtained by averaging over 100 realizations.
