利用洛伦兹水车研究混沌现象

Research on the chaos phenomena of Lorenz water wheel

洛伦兹水车是描述混沌系统的模型.本文从理论上分析了洛伦兹水车的运动方程,并制作了一台洛伦兹水车系统.用手机拍摄视频,再用视频分析软件Tracker追踪水车的运动状态,快速便捷地画出相应的相图,既出现混沌吸引子,又具有初值敏感性.通过对多个实验图像的分析,证明本系统为混沌系统.

Lorenz water wheel is a model to describe the chaotic system.The movement equations are analyzed and a Lorenz water wheel is set up.The video analysis software tracker is used to trace the motion of the water wheel recorded by a mobile phone.The corresponding physical images,such as phase diagrams,are drawed quickly and easily.Both the chaotic attractor and the initial value sensitivity have been found.Then the system has been proved to be a chaotic system by analyzing several experimental images.