有理差分方程全局渐近稳定性的一个新算法
A New Algorithm for Proving Global Asymptotic Stability of Rational Difference Equations
摘要：
有理差分方程的全局渐近稳定性是一个研究领域，已经得到很好的研究。与目前证明全局渐近稳定性的许多方法不同，我们提出了一种算法方法。我们在这里总结的算法采用了收缩的思想。给定一个特殊的有理差分方程，由一个将$k+1$维实数映射到其自身的函数$Q$定义，我们试图找到一个整数$K$，对于该整数，$Q^K$缩短了到差分方程的平衡点的距离。我们的算法已经能够证明一些一般性的结果，并提到我们的算法使用Maple的实施。
英文摘要：
Global asymptotic stability of rational difference equations is an area of research that has been well studied. In contrast to the many current methods for proving global asymptotic stability, we propose an algorithmic approach. The algorithm we summarize here employs the idea of contractions. Given a particular rational difference equation, defined by a function $Q$ which maps the $k+1$ dimensional real numbers to itself, we attempt to find an integer, $K$, for which $Q^K$ shrinks distances to the difference equation's equilibrium point. We state some general results that our algorithm has been able to prove, and also mention the implementation of our algorithm using Maple.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
