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熵是一种衡量数据不规则性的方法,是少有的判断混沌现象的定量指标之一。研究的目的是探明机构混沌运动以及在其混沌运动边缘熵值的变化情况。以小车直线一级倒立摆为研究对象,通过动力学仿真提取系统的动力响应时间序列,利用近似熵的方法,研究了小车一级倒立摆混沌边缘近似熵值的变化情况。主要研究结论是在系统的动态响应从周期运动到混沌运动的变换过程中,近似熵也经历了从0到大于0的变化;而在混沌边缘,出现了近似熵在0与大于0之间的交替变化,说明此时系统的周期运动与混沌运动共存。本文利用相轨迹法验证了结论的正确性。
Entropy is a measure of data irregularity and is one of the few quantitative indicators for judging chaos. The purpose of this study is to find out the change of institutional chaos and the entropy of the edge of its chaotic motion. Taking the in-line inverted pendulum as the research object, the dynamic response time series of the system are extracted through dynamic simulation. The approximate entropy method is used to study the change of the approximate entropy of the chaotic edge of the inverted pendulum. The main conclusion is that the approximate entropy also undergoes a change from 0 to more than 0 during the transformation of the system’s dynamic response from periodic motion to chaotic motion. On the edge of chaos, the approximate entropy appears between 0 and more than 0 Alternating changes, indicating that the system of periodic motion and chaos movement coexist. In this paper, the phase trajectory method to verify the conclusions of the correctness.