Emergence of Laplace-Distributed Growth Rates in Network Dynamics

The dynamical state of a complex network is rarely stationary in time, often exhibiting sufficiently erratic fluctuations so as to seem random. Previous observational studies on annual fish catches, flock sizes of migrating birds, and company sales have revealed that the growth rates follow a Laplace (double exponential) distribution, which is characterized by a higher probability of large increases/decreases relative to the Gaussian growth statistics predicted by typical null models. Yet despite the prevalence of Laplacian growth rates in disparate systems, their mechanistic origin has remained elusive. Here we show that Laplacian growth statistics emerge generically from the interplay between two ubiquitous features in real complex systems — multistability and noise. Under specific conditions, these factors combine to allow frequent transitions between the underlying attraction basins, which broadens tails of the growth distribution relative to that produced by a random walk. Our results suggests that “boom and bust” behavior may be the rule rather than the exception in networks with nonlinear dynamics, with implications for problems ranging from sustainable ecosystem management to financial system stability.