Extinction transition on diffusive substrate: a different universality class?

TL;DR

This paper investigates how diffusive heterogeneity influences the extinction transition in a one-dimensional system, revealing deviations from directed percolation universality due to local adaptation effects.

Contribution

It demonstrates that diffusive correlations in heterogeneity shift the transition point and alter the scaling behavior away from classical directed percolation predictions.

Findings

Transition point shifts due to diffusive heterogeneity

Density decay follows $t^{-0.159}$ at criticality

Scaling functions deviate from directed percolation predictions

Abstract

The extinction transition on a one dimensional heterogeneous substrate with diffusive correlations is studied. Diffusively correlated heterogeneity is shown to affect the location of the transition point, as the reactants adapt to the fluctuating environment. At the transition point the density decays like $t^{-0.159}$, as predicted by the theory of directed percolation. However, the scaling function describing the behavior away from the transition shows significant deviations from the DP predictions; it is suggested, thus, that the off-transition behavior of the system is governed by local adaptation to favored regions.