Eur. Phys. J. B 40, 313-319 (2004)
https://doi.org/10.1140/epjb/e2004-00279-5

Subcritical behavior in the alternating supercritical Domany-Kinzel dynamics

¹ Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, 2-1, Hirosawa, Wako, Saitama, 351-0198, Japan
² Aihara Complexity Modelling Project, ERATO, JST, 3–23–5 Uehara, Shibuya, Tokyo, 151-0067 Japan
³ Faculty of Engineering, Yokohama National University, 79-5, Tokiwadai, Hodogaya, Yokohama, 240-8501, Japan

Corresponding author: ^a masuda@brain.riken.jp

Received: 18 December 2003
Revised: 3 June 2004
Published online: 9 September 2004

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.