Subcritical behavior in the alternating supercritical Domany-Kinzel dynamics

TL;DR

This paper demonstrates that alternating supercritical cellular automata dynamics can lead to subcritical extinction behavior, revealing how environmental changes can paradoxically cause population collapse.

Contribution

It introduces a novel paradoxical phenomenon in cellular automata where periodic or random environmental changes induce extinction in otherwise stable populations.

Findings

Alternating supercritical dynamics can cause population extinction.

The phenomenon is general across original and reduced models.

Spatial extensions can realize Parrondo's paradox scenarios.

Abstract

Cellular automata are widely used to model real-world dynamics. We show using the Domany-Kinzel probabilistic cellular automata that alternating two supercritical dynamics can result in subcritical dynamics in which the population dies out. The analysis of the original and reduced models reveals generality of this paradoxical behavior, which suggests that autonomous or man-made periodic or random environmental changes can cause extinction in otherwise safe population dynamics. Our model also realizes another scenario for the Parrondo's paradox to occur, namely, spatial extensions.