Fig. 2
From: Taming out-of-equilibrium dynamics on interconnected networks
Comparison between the numerical and analytical calculations of the population flux. Population flux \(\dot{x}(t)\) (in absolute value, for clarity) as a function of the normalised connection strength \(\epsilon F/\Delta \lambda\) and the initial population distribution \({x}_{0}\) for two connected networks out of equilibrium. a, b Numerical calculation of \(\dot{x}(t)\) for two scale-free networks of \(N=250\) nodes (see caption of Fig. 1 for details), for \(t=1\) (a) and \(t=150\) (b). c, d Analytical approximation to \(\dot{x}(t)\) for the same situations. These plots show that Eq. (9) is in quantitative agreement with the numerical results, despite only depending on the first eigenvalues of networks \(A\) and \(B\), and the centrality of the connector nodes. In the numerical simulations (a–b), the connection strength \(\epsilon F\) has been modified by both changing the connector links (i.e., \(F\)) and the weight of the connector links (i.e., \(\epsilon\)). This way, we have gradually swept \(\epsilon F/\Delta \lambda\) from 0 to 1.
