文档介绍：II 基于 Matlab 的复摆混沌行为研究摘要自然界中存在无数的无序、非平衡和随机的复杂系统。混沌现象出现于非线性系统中, 它揭示了有序与无序的统一, 确定性与随机性的统一。混沌运动是非线性动力学系统所特有的复杂运动状态, 是一种貌似随机的不规则运动, 混沌的发现被誉为继相对论和量子力学后的第三次物理学革命, 混沌的研究一直备受学术界的关注。 Matlab 是一个适用于科学计算、工程设计、数值分析等领域的各种计算、演算和仿真分析的高性能的优秀数学软件。混沌理论研究的是非线性问题, 难以用解析式表达,只能采用数值解法,而 Matlab 在这方面便可展示其强大的潜能。本论文利用了 Matlab 软件研究经典的混沌现象的特征,并且对混沌的特点以及形成过程进行模拟分析研究;并用 Matlab 模拟了复摆运动行为及混沌现象, 对不同周期作出相图及奇怪吸引子, 可以看到随着外驱动力的增加,复摆振动逐渐由倍周期分岔走向混沌。关键词:混沌, Matlab ,复摆,倍周期分岔,奇怪吸引子 II II III III PLEX BEHAVIOR OF CHAOTIC PENDULUM BASED ON MATLAB ABSTRACT There are many disorders, non-equilibrium , random c omplex systems in the nature. Chaos appears in nonlinear systems, it reveals the unity of order and disorder, certainty and randomness of unity. Chaos isa nonlinear dynamic system unique to plex state of motion, isa 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 isa suitable for puting, engineering design, numerical analysis of the various fields puting, calculation and simulation analysis of high-quality mathematical software. Chaos t heory study nonlinear system which is difficult toe xpress use a nalytic style and colud only have n umerical solution , and Matlab will d emonstrate its strong potential in this respect . IV IV 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 VV 目录前言.............................................................................................................. 1 §