Figure 4

We are considering a model example with \(n=30\) agents, where the suitability landscape is given by the double well potential \(V(x,y)=(x^{2}-1)^{2}+y^{2}\) and the interaction radius is \(r=1\). In the first row, temporal snapshots of one realization of the process highlight its metastability. Due to the fast mixing in the well of the initial adopter, the innovation spreads quickly in the first well. In contrast, the transitioning between the two wells is a rare event, resulting in a large time gap for the innovation to spread from one well to the other. Then again, when the innovation has reached the second well, it will spread fast. The metastability of the spreading process is also confirmed in the plot of the evolution of the proportion of adopters. The 50 realizations (plotted in gray) out of an ensemble of 2000 simulations with the event-based approach for \(\Delta t=0.002\) show the fast spreading inside the wells and the exponential waiting time for the innovation to jump from one well to another