Critical behaviour of a probabilistic cellular automaton model for the dynamics of a population driven by logistic growth and weak Allee effect.
We investigate the critical behaviour of a one-parameter probabilistic mixture of one-dimensional elementary cellular automata under the guise of a model for the dynamics of a single-species unstructured population with nonoverlapping generations in which individuals have smaller probability of reproducing and surviving in a crowded neighborhood but also suffer from isolation and dispersal. Remarkably, the first-order mean field approximation to the dynamics of the model yields a cubic map containing terms representing both logistic and weak Allee effects. The model has a single absorbing state devoid of individuals, but depending on the reproduction and survival probabilities can achieve a stable population. We determine the critical probability separating these two phases and characterise the phase transition between them by finite-size scaling analysis of Monte Carlo data. The phase transition belongs to the directed percolation universality class of critical behaviour.
Publisher URL: http://arxiv.org/abs/1710.11305