[统计数据] 一类捕食者-食饵概率元胞自动机的稳定振荡； 平均场方法 [推广有奖]

摘要翻译：
我们分析了一个描述捕食者-食饵系统共存动力学的概率元胞自动机。在Lotka-Volterra模型的过程中，每个物种的个体被局部化在格点上，局部随机更新规则被启发。建立了两层平均场近似。简单近似等价于一个扩展的斑块模型，一个简单的集合种群模型，包括被猎物定殖的斑块、被捕食者定殖的斑块和空斑块。这种近似能够描述物种占有的有限可用空间。此外，对近似能够描述捕食者和食饵共存的两种类型：一类是种群密度在时间上恒定的，另一类是种群密度自持续的时间振荡。振荡与极限环相关，并通过Hopf分支产生。它们对初始条件的变化是稳定的，在这个意义上，它们不同于依赖于初始条件的Lotka-Volterra循环。在这方面，目前的模型比Lotka-Volterra模型在生物学上更符合实际。
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英文标题：
《Stable oscillations of a predator-prey probabilistic cellular automaton:
  a mean-field approach》
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作者：
T\^ania Tom\'e and Kelly C de Carvalho
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator-prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired on the processes of the Lotka-Volterra model. Two levels of mean-field approximations are set up. The simple approximation is equivalent to an extended patch model, a simple metapopulation model with patches colonized by prey, patches colonized by predators and empty patches. This approximation is capable of describing the limited available space for species occupancy. The pair approximation is moreover able to describe two types of coexistence of prey and predators: one where population densities are constant in time and another displaying self-sustained time-oscillations of the population densities. The oscillations are associated with limit cycles and arise through a Hopf bifurcation. They are stable against changes in the initial conditions and, in this sense, they differ from the Lotka-Volterra cycles which depend on initial conditions. In this respect, the present model is biologically more realistic than the Lotka-Volterra model.
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PDF链接：
https://arxiv.org/pdf/704.0512