离散随机Lotka-Volterra竞争系统参数的渐近性

The Asymptotic Characteristic of the Parameters of a Discrete Stochastic Lotka-VolterraCompetition System

Lotka-Volterra竞争系统是著名的人口动力系统模型之一。本文主要研究两种群Lotka-Volterra竞争系统。考虑到在实际中Lotka-Volterra竞争系统还受环境白噪声的影响,特别地,只需对白噪声的强度一个简单假设,就使得随机Lotka-Volterra模型的解随机最终有界。那么不同形式的环境白噪声是否会导致不同的结果,白噪声的出现是否会影响已有结论,并进行了研究。本文先对系统做变量替换,再通过重对数定律讨论了具有随机扰动的一个两种离散随机Lotka-Volterra竞争系统的参数的渐近性,主要结果以定理3给出。

Lotka-Volterra competition system is one of the famous population dynamic system models. In this paper, the Lotka-Volterra competition system about two populations is researched. Considering that Lotka-Volterra competition system is often affected by environment white noises in practice,particularly,the solution of the stochastic Lotka-Volt-erra competition system is random ultimately bounded when a simple assumption to the intensity of white noises is made. So different white noises will cause different results, then whether the appearance of white noises will affect the previous result, that needs to be studied. In this paper, firstly variable substitutions to the system are used, and then the asymptotic characteristic of the parameters of a discrete stochastic Lotka-Volterra competition system is discussed by Law of the iterated logarithm,the result is given by theorem 3.