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)EULEEJ0295-507510.1209/0295-5075/112/30002]. 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.



Research Center/Lab(s)

Center for High Performance Computing Research


This work was supported in part by the NSF under Grants No.PHY-1125915 and No. DMR-1506152 and by the Sao Paulo Research Foundation (FAPESP) under Grant No. 2017/08631-0. T.V. is grateful for the hospitality of the Kavli Institute for Theoretical Physics, Santa Barbara where part of the work was performed.

Keywords and Phrases

Intelligent systems; Population statistics, Critical behavior; Density fluctuation; Ensemble averages; Environmental noise; Evolution equations; External noise; Population sizes; Time-to-extinction, Monte Carlo methods

International Standard Serial Number (ISSN)

2470-0045: 2470-0053

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2018 American Physical Society (APS), All rights reserved.

Publication Date

01 Aug 2018

Included in

Physics Commons