Extinction transitions in correlated external noise

Abstract

We analyze the influence of long-range correlated (colored) external noise on extinction phase transitions in growth and spreading processes. Uncorrelated environmental noise (i.e., temporal disorder) was recently shown to give rise to an unusual infinite-noise critical point [Europhys. Lett. 112, 30002 (2015)]. It is characterized by enormous density fluctuations that increase without limit at criticality. As a result, a typical population decays much faster than the ensemble average which is dominated by rare events. Using the logistic evolution equation as an example, we show here that positively correlated (red) environmental noise further enhances these effects. This means, the correlations accelerate the decay of a typical population but slow down the decay of the ensemble average. Moreover, the mean time to extinction of a population in the active, surviving phase grows slower than a power law with population size. To determine the complete critical behavior of the extinction transition, we establish a relation to fractional random walks, and we perform extensive Monte-Carlo simulations.

arXiv comment11 pages, 12 figures, Final version

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• Reflected fractional Brownian motion in one and higher dimensions
• Probability density of the fractional Langevin equation with reflecting walls
• A comprehensive phase diagram for logistic populations in fluctuating environment
• Phase diagram for a logistic system under bounded stochasticity
• Non-Gaussian behavior of reflected fractional Brownian motion
• Critical properties of the Susceptible-Exposed-Infected model with correlated temporal disorder
• Influence of distinct kinds of temporal disorder in discontinuous phase transitions
• Connecting metapopulation heterogeneity to aggregated lifetime statistics
• Contact process with aperiodic temporal disorder