A mechanistic explanation for the emergence of Laplacian growth rates in complex systems

The state of a complex system is rarely stationary, often exhibiting large, seemingly erratic fluctuations. Nonetheless, observational studies of diverse systems have uncovered striking regularity in this randomness, finding that the growth rates of many real systems follow a universal Laplace (or "double exponential") distribution, characterized by heavier tails than a normal distribution. Here, we present a mechanistic explanation for this universal phenomenon. We show that the Laplacian growth statistics emerge from the interplay between multistability and noise, which can result in frequent transitions between attraction basins in a nonlinear system. This broadens the tail of the growth rate distribution as the possibility of extreme cases increases. We find that the exact shape of the fluctuation distribution is strongly influenced by the heterogeneity in network topology. Our results unveil the network characteristics that can control the frequency of transitions, potentially offering ways to predict the functioning of ecosystems, and guiding the design of technological systems tolerant to perturbations.