Influence of correlated temporal disorder on an extinction phase transition

We employ large-scale Monte Carlo simulations to investigate the effect of long-range correlated temporal disorder (i.e. external noise) on extinction phase transitions in the logistic evolution equation. Uncorrelated temporal disorder is known to cause an unusual phase transition controlled by an infinite-noise critical point [1]. It features diverging density fluctuations at criticality, implying that the typical population decay is much faster than the ensemble average. Our results demonstrate that correlated temporal disorder enhances these effects; the correlations further accelerate the decay of a typical population while slowing the decay of the ensemble average. We also establish a relation to reflected fractional Brownian motion [2] which yields a conjecture for the critical behavior of the population.

[1] T. Vojta and J.A. Hoyos Europhys. Lett. 112, 30002 (2015)
[2] A.H.O. Wada and T. Vojta Phys. Rev E 97, 020102 (2018)