Figure 7.

Representative time evolution of $\langle {\rho }_e\rangle$. Panel (a) corresponds to the active phase and panel (b) to the frozen phase (note the log-linear scale). All trajectories in both panels use the same value of $p=0.8$ and initial condition $x_0=0.5$ and ${\ell }_0=0.5$ but different realizations of the network and the dynamics. In both cases, the averages use 100 runs that did not end in the frozen phase. In panel (b) we observe an exponential behavior $\langle {\rho }_e\rangle \propto e^{-t/{\tau }_0}$ with a small dependence of ${\tau }_0$ with system size. In panel (a), the fluctuations of $\langle {\rho }_e\rangle$ around the well defined value decrease with system size.