一个截断误差诱导下的随机数字振荡系统  

A stochastic digital oscillating system induced by the truncation error

作　　者：盛利元[1] 贾伟尧[1] 

机构地区：[1]中南大学物理科学与技术学院,长沙410083

出　　处：《物理学报》2005年第12期5574-5580,共7页Acta Physica Sinica

基　　金：湖南省自然科学基金(批准号:04JJ3077)资助的课题.~~

摘　　要：计算机截断误差通常被认为会导致混沌系统退化.根据这种认识,提供了一个完全由计算机截断误差诱导的简单系统走向复杂化或混沌的反例.该系统定义为椭圆反射腔映射系统的过焦系统,理论解为一个极限序列,对应计算机解则是一个随机数字振荡系统.分析表明,计算机解是在截断误差诱导下由理论解变异而来的.理论解中系统存在“回转机制”,截断误差诱导系统在非双曲性不动点局域产生“逃逸机制”,从而发现一种阵发混沌的新机制.It is generally believed that chaotic systems will collapse due to computer truncation error. In this paper we introduce a contrary example, in which a simple system is induced to complication or chaos completely by computer truncation. The system is defined as a cross-focus system in elliptical reflecting cavity map system. The theoretical solution is a limiting sequence and the computer solution is a stochastic digital oscillating system induced from the theoretical solution by truncation error. There is only a turn-round mechanism in the system theoretically. On the other hand, round-off induces the nonhyperbolic fixed points in the system to produce a new escape mechanism of intermittent chaos.

关 键 词：截断误差 切延迟椭圆反射腔映射系统 随机振荡 阵发混沌 

分 类 号：TP399[自动化与计算机技术—计算机应用技术]