Antal T, Droz M
Département de Physique Théorique, Université de Genève, CH 1211 Genève 4, Switzerland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 May;63(5 Pt 2):056119. doi: 10.1103/PhysRevE.63.056119. Epub 2001 Apr 20.
A coarse grained description of a two-dimensional prey-predator system is given in terms 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.
通过一个包含两个控制参数（猎物和捕食者的扩散率）的简单三态晶格模型，给出了二维猎物 - 捕食者系统的粗粒度描述。通过动态平均场近似和广泛的数值模拟研究了该模型的性质。结果表明，稳态相图分为两个相：纯猎物相和猎物与捕食者共存相，其中可能存在时间和空间振荡。除了通常的类似定向渗流的转变外，该系统还表现出一种意想不到的、不同类型的向猎物吸收相的转变。从共存相的振荡域到非振荡域的转变被描述为一种交叉现象，即使在无限尺寸极限下也依然存在。讨论了有限尺寸效应的重要性，并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据，以解释导致局部和全局振荡的潜在机制。
