2017/03/31 by J. Ricardo G. Mendonça, Yeva Gevorgyan
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Allee effect #Applied mathematics #Cellular Automata and Applications #Cellular automaton #Computer science #Discrete time and continuous time #Dynamics (music) #Mathematics #Physics #Population #Probabilistic logic #Statistical physics #Statistics #Stochastic cellular automaton #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #nlin.CG
paper · pdf · doi:10.1103/physreve.95.052131
published as Phys. Rev. E 95, 052131 (2017) · REVTeX 4.1, 10 pages, 5 figures, 64 references. Version (v3) corresponds, except for a few words and two references, to the published version
arxiv created 2017/05/18 · openalex publication_date 2017/05/18 · arxiv updated 2017/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with nonoverlapping generations. Beginning with a general six-parameter model, we find constraints on the transition probabilities of the PCA that guarantee that the ensuing approximations make sense in terms of population dynamics and classify the valid combinations thereof. Several possible models display a negative cubic term that can be interpreted as a weak Allee factor. We also investigate the conditions under which a one-parameter PCA derived from the more general six-parameter model can generate valid population growth dynamics. Numerical simulations illustrate the behavior of some of the PCA found.