Emergence of Laplace-Distributed Growth Rates in Complex Systems

Speaker: Sean P. Cornelius (Ryerson)

Abstract: The dynamical state of a complex network is rarely stationary in time, often exhibiting fluctuations that are sufficiently erratic so as to seem random. Previous observational studies have nonetheless discovered a surprising degree of regularity, finding that the statistics of the underlying growth rates of many systems follow a so-called Laplace (double exponential) distribution, which is characterized by a higher probability of large increases/decreases than a normal distribution. This phenomenon has been found in systems as diverse as annual fish catches, flock sizes of migrating birds and the sales of companies. Despite this ubiquity, however, a universal generative mechanism has remained elusive. Here we show that that Laplacian growth statistics arise naturally from two ingredients–multistability and noise. These features are common to a broad range of systems, and can conspire to produce a nontrivial probability of extreme fluctuations. Our findings suggest that “boom and bust” dynamics may be the rather than the exception in real complex systems, with implications for problems ranging form sustainable ecosystem management to financial system stability.