A probabilistic cellular automata model for the dynamics of a population driven by logistic growth and weak Allee effect

Autor(es)

Mendonca, J. R. G.

• Tipo de documento: Artigo Científico
• Fonte: Journal of Physics A-Mathematical and Theoretical; v. 51, n. 14 APR 6 2018.
• Citações Web of Science: 2

Resumo

We propose and investigate 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 neighbourhood 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 find that the phase transition between them is in the directed percolation universality class of critical behaviour. (AU)

• Processo FAPESP: 15/21580-0 - Análise e simulação de passeios aleatórios e processos de exclusão sobre grafos
• Beneficiário: José Ricardo Gonçalves de Mendonça
• Linha de fomento: Auxílio à Pesquisa - Regular