Phase transitions and oscillations in a lattice prey-predator model
Phase transitions and oscillations in a lattice prey-predator model
复制标题
DOI：
10.1103/physreve.63.056119
复制
发表时间：
2001-05-01
影响因子：
2.4
通讯作者：
Droz, M
中科院分区：
文献类型：
--
作者：
Antal, T;Droz, M
在一个简单的三态格子模型中给出了一个二维捕食系统的粗粒度描述，该模型包含两个控制参数：捕食者和被捕食者的传播率。通过动态平均场近似和大量的数值模拟研究了该模型的性质。结果表明，定态相图分为两个阶段：纯捕食者阶段和捕食者与被捕食者共存阶段，这两个阶段存在时间和空间上的振荡。除了通常的定向渗流转变外，系统还表现出一种意想不到的、不同类型的到猎物吸收阶段的转变。从共存相的振荡域到非振荡域的穿越被描述为一种交叉现象，即使在无限大的尺寸限制下，这种交叉现象仍然存在。讨论了有限尺寸效应的重要性，建立了不同量之间的标度关系。最后，基于模型的空间结构，给出了物理论证，以解释导致局部和全球振荡的潜在机制。
A coarse grained description of a two-dimensional prey-predator system is given in tens of a simple three-state lattice model containing two control parameters: the spreading rates of prey and predator. The properties of the model are investigated by dynamical mean-field approximations and extensive numerical simulations. It is shown that the stationary state phase diagram is divided into two phases: a pure prey phase and a coexistence phase of prey and predator in which temporal and spatial oscillations can be present. Besides the usual directed percolationlike transition, the system exhibits an unexpected, different type of transition to the prey absorbing phase. The passage from the oscillatory domain to the nonoscillatory domain of the coexistence phase is described as a crossover phenomena, which persists even in the infinite size limit. The importance of finite size effects are discussed, and scaling relations between different quantities are established. Finally, physical arguments, based on the spatial structure of the model, are given to explain the underlying mechanism leading to local and global oscillations.