《14-The-Lorenz-System_2016_Differential-Equations-Dynamical-Systems-and-an-Introduction-to-Chaos》.pdf
- 1、本文档共24页,可阅读全部内容。
- 2、有哪些信誉好的足球投注网站(book118)网站文档一经付费(服务费),不意味着购买了该文档的版权,仅供个人/单位学习、研究之用,不得用于商业用途,未经授权,严禁复制、发行、汇编、翻译或者网络传播等,侵权必究。
- 3、本站所有内容均由合作方或网友上传,本站不对文档的完整性、权威性及其观点立场正确性做任何保证或承诺!文档内容仅供研究参考,付费前请自行鉴别。如您付费,意味着您自己接受本站规则且自行承担风险,本站不退款、不进行额外附加服务;查看《如何避免下载的几个坑》。如果您已付费下载过本站文档,您可以点击 这里二次下载。
- 4、如文档侵犯商业秘密、侵犯著作权、侵犯人身权等,请点击“版权申诉”(推荐),也可以打举报电话:400-050-0827(电话支持时间:9:00-18:30)。
查看更多
《14-The-Lorenz-System_2016_Differential-Equations-Dynamical-Systems-and-an-Introduction-to-Chaos》.pdf
14
The Lorenz System
So far, in all of the differential equations we have studied, we have not encoun-
tered any “chaos.” The reason is simple: The linear systems of the first few
chapters always have straightforward, predictable behavior. (OK, we may see
solutions wrap densely around a torus as in the oscillators of Chapter 6, but
this is not chaos.) Also, for the nonlinear planar systems of the last few chap-
´
ters, the Poincare–Bendixson Theorem completely eliminates any possibility
of chaotic behavior. So, to find chaotic behavior, we need to look at nonlinear,
higher-dimensional systems.
In this chapter we investigate the system that is, without doubt, the most
famous of all chaotic differential equations, the Lorenz system from meteorol-
ogy. First formulated in 1963 by E. N. Lorenz as a vastly oversimplified model
of atmospheric convection, this system possesses what has come to be known
as a strange attractor. Before the Lorenz model started making headlines, the
only types of stable attractors known in differential equations were equilibria
and closed orbits. The Lorenz system truly opened up new horizons in all areas
of science and engineering, as many of the phenomena present in the Lorenz
system have later been found in all of the areas we have previously investigated
(biology, circuit theory, mechanics, and elsewhere).
In the ensuing nearly 50 years, much progress has been made in the study
of chaotic systems. Be forewarned, however, that the analysis of the chaotic
behavior of particular systems, such as the Lorenz system, is usually extremely
difficult. Most of the chaotic behavior that is readily understandable arises
from geometric models for particular differential equations, rather than from
Differential Equations, Dynamical Systems, and an Introduction to Chaos. DOI: 10.1016/B978-0-12-382010-5.00014-2
c
2013 Elsevier Inc. All right
您可能关注的文档
- 《06SG432-1(预应力溷凝土双T板-坡板_宽度2.4m)》.pdf
- 《07-PHP操作MySQL》.doc
- 《07-PP-CM采购与应付矩证-091022》.xls
- 《07.Deep Learning in Action_肖达》.ppt
- 《07.pp87100 _A10_无刷直流马达控制晶片之设计_》.pdf
- 《070801中兴TD-SCDMA无线网络规划介绍厦门网通》.pdf
- 《07_SQL-数据查询》.ppt
- 《07程千帆全集第七卷:閒堂文薮》.pdf
- 《08 fundamentals of multichip packaging》.pdf
- 《08 电影中的_MTV美学_质问一种电影批评谬见》.pdf
文档评论(0)