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The '''Lorenz system''' is a system of [[ordinary differential equation]]s first studied by [[Edward Norton Lorenz|Edward Lorenz]]. It is notable for having [[Chaos theory|chaotic]] solutions for certain parameter values and initial conditions. In particular, the '''Lorenz attractor''' is a set of chaotic solutions of the Lorenz system. In popular media the "[[butterfly effect]]" stems from the real-world implications of the Lorenz attractor, i.e. that in any physical system, in the absence of perfect knowledge of the initial conditions (even the minuscule disturbance of the air due to a butterfly flapping its wings), our ability to predict its future course will always fail. This underscores that physical systems can be completely deterministic and yet still be inherently unpredictable even in the absence of quantum effects. The shape of the Lorenz attractor itself, when plotted graphically, may also be seen to resemble a butterfly.
The '''Lorenz system''' is a system of [[ordinary differential equation]]s first studied by [[Edward Norton Lorenz|Edward Lorenz]]. It is notable for having [[Chaos theory|chaotic]] solutions for certain parameter values and initial conditions. In particular, the '''Lorenz attractor''' is a set of chaotic solutions of the Lorenz system. In popular media the "[[butterfly effect]]" stems from the real-world implications of the Lorenz attractor, i.e. that in any physical system, in the absence of perfect knowledge of the initial conditions (even the minuscule disturbance of the air due to a butterfly flapping its wings), our ability to predict its future course will always fail. This underscores that physical systems can be completely deterministic and yet still be inherently unpredictable even in the absence of quantum effects. The shape of the Lorenz attractor itself, when plotted graphically, may also be seen to resemble a butterfly.
“洛伦兹系统”是由[[爱德华-诺顿-洛伦兹|爱德华-洛伦兹]]最先提出的一种由[[常微分方程]]构成的系统。值得注意的是，在一些特定参数和初始条件下，它的解是[[混沌理论|混沌]]的。更确切的说，“洛伦兹吸引子”其实是洛伦兹系统所有的混沌解。人们通常所说的"[[蝴蝶效应]]"源于洛伦兹吸引子的现实意义：即在任何物理系统中，在对初始条件不完全了解的情况下，即使是蝴蝶拍打翅膀引起的微小扰动都可以让我们无法成功的预测系统的未来进程。对物理系统来说，即使它可以被完整的测定，但人们仍然不能完全预测它（即使排除了量子效应也不行）。洛伦兹吸引子绘制成的图形看起来就像一只蝴蝶。这也是“蝴蝶效应”这一词的由来。（关于这一词的由来需要参考书籍《The essence of chaos》）
“洛伦兹系统”是由[[爱德华-诺顿-洛伦兹|爱德华-洛伦兹]]最先提出的一种由[[常微分方程]]构成的系统。值得注意的是，在一些特定参数和初始条件下，它的解是[[混沌理论|混沌]]的。更确切的说，“洛伦兹吸引子”其实是洛伦兹系统所有的混沌解。人们通常所说的"[[蝴蝶效应]]"源于洛伦兹吸引子的现实意义：即在任何物理系统中，在对初始条件不完全了解的情况下，即使是蝴蝶拍打翅膀引起的微小扰动都可以让我们无法成功的预测系统的未来进程。对物理系统来说，即使它可以被完整的测定，但人们仍然不能完全预测它（即使排除了量子效应也不行）。洛伦兹吸引子绘制成的图形看起来就像一只蝴蝶。这也是“蝴蝶效应”这一词的由来。
（关于这一词的由来需要参考书籍《The essence of chaos》）引用原文如下：(未翻译)The thing that has made the origin of the phrase a bit uncertain
is a peculiarity of the first chaotic system that I studied in detail.
Here an abbreviated graphical representation of a special collection
of states known as a “strange attractor” was subsequently found
to resemble a butterfly, and soon became known as the butterfly.
In Figure 2 we see one butterfly; a representative of a closely related
species appears on the inside cover of Gleick’s book. A number of
people with whom I have talked have assumed that the butterfly
effect was named after this attractor. Perhaps it was.
Some correspondents have also called my attention to Ray
Bradbury’s intriguing short story “A Sound of Thunder,” written
long before the Washington meeting. Here the death of a prehistoric
butterfly, and its consequent failure to reproduce, change the
outcome of a present-day presidential election.
Before the Washington meeting I had sometimes used a sea gull
as a symbol for sensitive dependence. The switch to a butterfly was
actually made by the session convenor, the meteorologist Philip
Merilees, who was unable to check with me when he had to submit
the program titles. Phil has recently assured me that he was not
familiar with Bradbury’s story. Perhaps the butterfly, with its
seeming frailty and lack of power, is a natural choice for a symbol
of the small that can produce the great.
Other symbols have preceded the sea gull. In George R.Stewart’s
novel Storm, a copy of which my sister gave me for Christmas when
she first learned that I was to become a meteorology student, a
meteorologist recalls his professor’s remark that a man sneezing in
China may set people to shoveling snow in New York. Stewart’s
professor was simply echoing what some real-world meteorologists
had been saying for many years, sometimes facetiously, sometimes
seriously
==概述==
==概述==
* {{cite journal |last1=Viana |first1=Marcelo |title=What's new on Lorenz strange attractors? |journal=The Mathematical Intelligencer |date=2000 |volume=22 |issue=3 |pages=6–19|doi=10.1007/BF03025276 }}
* {{cite journal |last1=Viana |first1=Marcelo |title=What's new on Lorenz strange attractors? |journal=The Mathematical Intelligencer |date=2000 |volume=22 |issue=3 |pages=6–19|doi=10.1007/BF03025276 }}
* {{cite journal|last1=Lorenz|first1=Edward N.|author1-link=Edward N. Lorenz|title=The statistical prediction of solutions of dynamic equations.|journal=Symposium on Numerical Weather Prediction in Tokyo|year=1960|url=http://eaps4.mit.edu/research/Lorenz/The_Statistical_Prediction_of_Solutions_1962.pdf}}
* {{cite journal|last1=Lorenz|first1=Edward N.|author1-link=Edward N. Lorenz|title=The statistical prediction of solutions of dynamic equations.|journal=Symposium on Numerical Weather Prediction in Tokyo|year=1960|url=http://eaps4.mit.edu/research/Lorenz/The_Statistical_Prediction_of_Solutions_1962.pdf}}
* {{cite book | last1=N.Lorenz | first1=Edward | title=The Essence of Chaos | publisher=UCL Press | isbn=978-1-85-728454-6 | year=1993}}
== Further reading ==
== Further reading ==