基于Malab的复摆混沌行为研究.doc

基于Matlab的复摆混沌行为研究 摘 要 自然界中无序、非平衡和随机的。the complex behavior of chaotic pendulum based on mATLAB ABSTRACT There are many disorders, non-equilibrium, random complex systems in the nature. Chaos appears in nonlinear systems, it reveals the unity of order and disorder, certainty and randomness of unity. Chaos is a nonlinear dynamic system unique to the complex state of motion, is a seemingly random, irregular motion, chaos, following the discovery of relativity and quantum mechanics known as the third after the revolution in physics, Chaos has always been of academic attention. Matlab is a suitable for scientific computing, engineering design, numerical analysis of the various fields of computing, calculation and simulation analysis of high-quality mathematical software.Chaos theory study nonlinear system which is difficult to express use analytic style and colud only have numerical solution, and Matlab will demonstrate its strong potential in this respect. In this thesis, a Matlab software for classical chaos characteristics, and the chaos of the characteristics and formation process of simulation studies; and use Matlab to simulate the pendulum movement behavior and chaotic phenomena, on different cycles to the phase diagram and the strange attractor, As you can see the increase in external driving force, pendulum vibration gradually from period-dou -bling bifurcation to chaos. Key words: Chaos, Matlab,compound pendulum,bifurcation,strange attractor 目 录 前 言 1 §1.2.4 M文件及程序调试 2 §1.4 本章小结 5 第二章 混沌行为与特性 5 §2.1 混沌理论 5 §2.1.1 简单的数学游戏 6 §2.1.2 “蝴蝶效应” 7 §2.2 用Matlab演示混沌的基本性质 8 §2.2.1 用Matlab产生标准的混沌信号 8 §2.2.2 倍周期分岔——通向混沌之路 9 §2.2.3 初值敏感性 12 §2.3 本章小结 13 第三章 用Matlab模拟复摆振动中的混沌行为 13 §3.1 复摆运动模型与振动方程 14 §3.2 复摆运动状态的模拟研究 15 §3.2.1 无驱动力无阻尼的复摆运动 15 §3.2.2 无驱动力有阻尼的复摆运动 17 §3.2.3 有驱动力有阻尼的复摆运动，受迫运动 19 §3.3 本章小结 25 结 论 27 参考文献 28 致 谢 29 前 言 自然界中无序、非平衡和随机的。Matlab是集数值运算、符号运算、数据可视化、数据图文字统一处理、系统动态仿真等功能于一体的数学软件，具有很高的编程效率，在线性代数、矩阵分析、数值计算及优化、系统动力学、建模与仿真等领域中得到广泛应用。混沌理论研究的是非线性问题，难以用解析式表达，只能采