食饵-捕食者生物群系动力学的Bragg-Williams近似
Bragg-Williams approximation for the dynamics of prey-predator biological associations
摘要：
从理论上研究了相互作用的生物物种的联合动力学。我们探讨了一个平均场近似描述的时间演化的生态系统的基本捕食者物种间的关系，以及近似引入时间相关性的动态。首先，我们讨论的解决方案的Volterra-Lotka模型在平均场近似的基础上，在类比与Weiss解决方案的伊辛模型的铁磁材料。为了探讨长程时间关联的影响，我们描述了一种布拉格-威廉姆斯近似下的系统的时间演化。这种方法使我们能够评估生态系统的特征寿命。这一数量对于讨论生态系统在各种环境条件下的时间演化是非常有用的，而这通常是不被考虑的。我们讨论了一般趋势的时间演变的关联与一些数据从实际生态系统。
英文摘要：
The dynamics of an association of interactive biological species is studied theoretically. We explore a mean field approximation to describe the temporal evolution of an ecological system with the basic prey-predator interspecies relation, as well as an approximation to introduce time correlations in the dynamics. We start by discussing the solution of the Volterra-Lotka model in a mean field approximation based in an analogy with the Weiss solution to the Ising model for ferromagnetic materials. In order to explore the effects of long-range time correlations, we describe the time evolution of the system within a kind of Bragg-Williams approximation. This approach allows us to evaluate a characteristic life-time of the ecosystem. This quantity could be very useful to discuss the time evolution of the system under a wide diversity of environmental conditions of the ecosystem which is not usually considered. We discuss the general trends of the temporal evolution of the association with some data from real ecosystems.
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