Fig 1.
Typical time development of the number of nodes in state 1.
N(1) decreases over time, until there is a critical transition at t = Tc (red vertical line). When looking at the standard deviation and the autocorrelation of N(1), one can see that it increases significantly prior to the critical transition, which constitutes an EWS.
Fig 2.
Natural and effective state of the system.
N(1) and behave similarly, however, the effective state has a higher variance.
Fig 3.
An increase in standard deviation as well as autocorrelation can be observed prior to the critical transition, both for the natural state N(1) (blue) and the effective state (green) in networks with γ = 9.
Fig 4.
An increase in standard deviation as well as autocorrelation can be observed prior to the critical transition, both for the natural state N(1) (blue) and the effective state (green) in networks with γ = 5.
Fig 5.
An increase in standard deviation as well as autocorrelation can be observed prior to the critical transition, both for the natural state N(1) (blue) and the effective state (green) in networks with γ = 3. Note that the effective state shows a much clearer signal with less fluctuations than the natural state.
Fig 6.
While the natural state of the system N(1) (blue) shows no EWS (both standard deviation and autocorrelation decrease), the EWS are clearly visible for the effective state (green) in networks with γ = 2.