平均空间占有量对混沌的度量——均匀度理论之应用

Chaos Interpreted by the Average Monopolized Space——Application of Uniformity Theory

对于一条离散的、混沌的轨道,独占球体积是轨道上一个点的空间占有量,k步混沌强度(kSCM)是轨道的平均空间占有量,它被用于度量混沌轨道的特征.取k=400,应用400步混沌强度(400SCM),对Lorenz系统和Henon map进行分析,400SCM与李亚普诺夫指数有相似的走势.Lorenz系统的Prandtl数a与400SCM的关系是单调的,Rayleigh数b在[12,28]的区间上是混沌的,没有准周期窗口,但参数c与400SCM的关系不是单调的,说明在c∈[2.666,4.566]区间上,准周期窗口与混沌窗口交错.对Henon map的计算结果表明b=1.7和a=1.3附近存在准周期窗口.基于上述计算结果得出k步混沌强度能够准确度量混沌特征.

To a discrete and chaotic orbit, monopolized sphere capacity is the monopolized space of a point on the orbit, k step chaometry（kSCM） is the average monopolized space of the orbit, which is used to measure the characteristics of the chaotic orbit. Let k = 400, 400SCM was used to analyze Lorenz system and Henon map. The results show that 400SCM and Lyapunov exponent trend similarly. The relations between b and 400SCM of Lorenz system are monotone, there is no quasi-periodic window in b ∈[12,18]. But the relations between c and 400SCM are not the same, which show that there are quasi-periodic and chaotic windows alternately in c ∈[2. 666,4. 566]. Based on the symulation of Henon map, there are quasi-periodic windows about b = 1.7 and a = 1.3. It is concluded that k step chaometry can be used to measure the chaotic characteristcs of a dynamic system.