近似概率元胞自动机在离散Logistic增长下的单种群动态
Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete logisticlike growth with and without weak Allee effects
摘要：
我们研究一维初等概率元胞自动机（PCA），其动力学在一阶平均场近似产生离散的logisticlike增长模型的单物种非结构化人口与非重叠世代。从一个一般的六参数模型开始，我们找到了PCA的转移概率的约束条件，保证了随后的近似在种群动态方面是有意义的，并对其有效组合进行分类。几种可能的模型显示负的三次项，可以解释为弱Allee因子。我们还研究了条件下，一个参数PCA来自更一般的六参数模型可以产生有效的人口增长动力学。数值模拟说明了一些PCA发现的行为。
英文摘要：
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.
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