一种简易自组混沌摆的相关参量研究

STUDY ON RELEVANT PARAMETERS OF SIMPLE SELF-ASSEMBLING CHAOTIC PENDULUM

作为动力系统理论的一个重要分支,混沌学在物理、信息、金融、人工智能等领域的交叉发展越来越重要。在实验室自组的可变参数的混沌摆实验装置的前期工作基础上,本文首先从动力学方程出发模拟了驱动力频率、驱动臂臂长、转动惯量和阻尼项改变的分岔图,探究运动系统通往混沌的倍周期之路,进而通过实验研究了转动惯量和阻尼项对于系统运动的影响。实验与模拟结果均表明随着上述实验参数的变化摆的运动状态在混沌与周期运动之间反复变化,而且这种变化是突变的。通过摄像和追踪质点的方法,绘制相图并将动力学方程的数值模拟结果与实验数据进行比较。该装置可以作为本科生认识复杂系统的入门内容。

As an important branch of dynamical systems theory,the intersection of chaos science is becoming more and more important in the fields of physics,information,finance,artificial intelligence and so on.Based on the preliminary work of the laboratory self-assembled multi-parameter chaotic pendulum experimental device,this paper firstly simulates the bifurcation diagrams from the dynamical equations with the change of driving force frequency,length of the driving arm,rotational inertia and damping term,and explores the multiplicative cycle path of the motion system to chaos.Then we investigate the effects of rotational inertia and damping term on the motion of the system by experiments.Both experimental and simulation results show that the motion state of the pendulum changes repeatedly between chaotic and periodic motion with the change of above experimental parameters,and this change is abrupt.The phase diagrams were drawn through videotaping and mass-tracking,and numerical simulation results of the dynamical equations were compared with the experimental data.This device can be used as an introduction for undergraduate students to understand complex systems.