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.
A. H. Wada et al., "Extinction Transitions in Correlated External Noise," Physical Review E, vol. 98, no. 2, American Physical Society (APS), Aug 2018.
The definitive version is available at https://doi.org/10.1103/PhysRevE.98.022112
Center for High Performance Computing Research
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)
Article - Journal
© 2018 American Physical Society (APS), All rights reserved.
01 Aug 2018
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.