Department of Mathematics and NTIS, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 8,306 14 Plzeň, Czech Republic.
Math Biosci Eng. 2022 Apr 13;19(6):6072-6087. doi: 10.3934/mbe.2022283.
In this paper, we study stationary patterns of bistable reaction-diffusion cellular automata, i.e., models with discrete time, space and state. We show the rich variability based on the interplay of the capacity and viability and the specific form of reaction functions. While stationary k-periodic patterns occur naturally in many situations in large (exponential) numbers, there exist extreme situations for which there are no heterogeneous patterns. Moreover, nonmonotone dependence of the number of stationary patterns on the diffusion parameter is shown to be natural in the fully discrete setting.
在本文中，我们研究了双稳反应扩散元胞自动机的定态模式，即具有离散时间、空间和状态的模型。我们基于容量和生存力的相互作用以及反应函数的特定形式展示了丰富的可变性。虽然在许多情况下，大（指数）数量的自然会出现定态 k 周期模式，但也存在不存在异质模式的极端情况。此外，在完全离散的设置中，定态模式的数量对扩散参数的非单调依赖性是自然的。
