物流增长的巨大波动
Giant fluctuations in logistic growth
摘要：
我们分析的波动时，两个竞争的物种，最初的几个个体，提交给一个逻辑增长的个体数量。我们发现，当总的个人数量达到承载能力，每个物种的数量受到巨大的波动（方差$\sim$平均2），如果两个物种有相似的增长率。我们发现，只有当增长率显着不同时，才可以使用确定性的逻辑方程，否则这种增长必须由随机过程工具进行研究。这些结果推广到一个广泛的一类增长规律。
英文摘要：
We analyze the fluctuation of the number of individuals when two competing species, beginning with a few initial individuals, are submitted to a logistic growth. We show that when the total number of individuals reaches the carrying capacity, the number of each species is subject to giant fluctuations (variance $\sim$ mean 2) if the two species have similar growth rate. We show that the deterministic logistic equation can be used only when the growth rates are significantly different, otherwise such growth has to be investigated by stochastic processes tools. These results generalize to a wide class of growth law.
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