Rare events in “noisy” networks (Vol. 49, No. 3)

The average extinction time, , for a regular network versus the number of nodes, N, and several amplitudes of external noise, D.

Bringing diseases to extinction and mitigating the effects of human-caused environmental changes which accelerate the rate of species extinction are issues of worldwide importance. Both phenomena are typically rare events, relying on the interplay between network topology, nonlinear dynamics, and random fluctuations from the environment and interactions. However, the prediction of such rare events in general stochastic networks was an unsolved problem, despite extensive work in network dynamics. Here we solve the problem of predicting rare events as large fluctuations from metastable states with a general theory that combines mean-field approximations, large-deviation techniques and network topology. A benefit of our approach is its flexibility in describing the effects of multiple sources of different continuous and discrete noise. Using our theory, we demonstrate that networks with both internal interaction noise and external parameter noise exhibit a cross-over where the familiar exponential scaling of rare-event times with the number of nodes in the network is lost, and parametric noise dominates.

J. Hindes and I. B. Schwartz, Rare events in networks with internal and external noise, EPL 120, 56004 (2017)