LMGS吸引子混沌特征的定量观测

Quantitative Observation of the Chaos Characteristics of the LMGS Attractors

对孙海坚等人给出的Logistic映射图形集 (theLogisticMapGraphSet ,简称LMGS)的定义进行了扩展 ,并利用扩展的LMGS的定义构造出许多美丽的 2 D LMGS图形·这些美丽的图形根据其生成方式不同 ,可分成两类图形和吸引子·本文探讨了图形与吸引子之间的联系 ,发现图形的边缘与其对应的吸引子相似 ;并由一维可观察量计算系统混沌定量判据的方法 ,计算了吸引子的Lyapunov指数和关联维数 。

The definition of the logistic map graph set (it is called LMGS for short) was expanded, and a lot of beauty 2 D LMGS graphs were generated by using the expanded definition.According to different generated form,these beauty graphs can be classified into two categories:graph and the attractor of the graph.The relationship between graph and the attractor of the graph was investigatecl.The graph boundary is similar with the attractor of the graph.The largest lyapunov exponent and the correlation dimension of the attractor of the graph were calculated by determining the chaos quantitative criterion of the system by one freedom degree times series.The attractor of the graph has chaos dynamic characteristics.