Stochastic Spatial Model of Producer-Consumer Systems on the Lattice
Stochastic Spatial Model of Producer-Consumer Systems on the Lattice
复制标题
格子上生产者-消费者系统的随机空间模型
DOI：
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发表时间：
2013
影响因子：
1.2
通讯作者：
N. Lanchier
中科院分区：
文献类型：
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作者：
N. Lanchier
本文的目的是给一个严格的分析的随机空间模型的生产者-消费者系统，最近已经介绍了康和作者，以了解空间的作用，在生态社区中的个人竞争资源。正方形格子的每个点被一个个体占据，该个体的特征在于两种可能类型之一，并且以速率1连续更新其类型。每个个体被认为是资源的生产者和消费者，每次更新时的新类型是根据与邻居消耗由要更新的个体产生的资源的能力成比例的概率从某个交互邻居中随机选择的。除了给出一个完整的定性图片的空间模型的相图，我们的研究结果表明，非空间确定性的随机过程的平均场近似未能描述的行为的系统中存在的局部相互作用。特别是，我们证明了，在非空间模型显示双稳态的参数区域，有一个占主导地位的类型，无论其初始密度在空间模型中获胜，并列入空间也转化为两种类型共存的参数区域显着减少。
The objective of this paper is to give a rigorous analysis of a stochastic spatial model of producer-consumer systems that has been recently introduced by Kang and the author to understand the role of space in ecological communities in which individuals compete for resources. Each point of the square lattice is occupied by an individual which is characterized by one of two possible types, and updates its type in continuous time at rate 1. Each individual being thought of as a producer and consumer of resources, the new type at each update is chosen at random from a certain interaction neighborhood according to probabilities proportional to the ability of the neighbors to consume the resource produced by the individual to be updated. In addition to giving a complete qualitative picture of the phase diagram of the spatial model, our results indicate that the nonspatial deterministic mean-field approximation of the stochastic process fails to describe the behavior of the system in the presence of local interactions. In particular, we prove that, in the parameter region where the nonspatial model displays bistability, there is a dominant type that wins regardless of its initial density in the spatial model, and that the inclusion of space also translates into a significant reduction of the parameter region where both types coexist.