在非线性科学中，“混沌”这个词的含义和本意相似但又不完全一致，非线性科学中的混沌现象指的是一种确定的但不可预测的运动状态。它的外在表现和纯粹的随机运动很相似，即都不可预测。但和随机运动不同的是，混沌运动在动力学上是确定的，它的不可预测性是来源于运动的不稳定性。或者说混沌系统对无限小的初值变动和微绕也具于敏感性，无论多小的扰动在长时间以后，也会使系统彻底偏离原来的演化方向。混沌现象是自然界中的普遍现象，天气变化就是一个典型的混沌运动。混沌现象的一个著名表述就是蝴蝶效应：南美洲一只蝴蝶扇一扇翅膀，就会在佛罗里达引起一场飓风。 　　混沌系统具有三个关键要素：一是对初始条件的敏感依赖性；二是临界水平，这里是非线性事件的发生点；三是分形维，它表明有序和无序的统一。混沌系统经常是自反馈系统，出来的东西会回去经过变换再出来，循环往复，没完没了，任何初始值的微小差别都会按指数放大，因此导致系统内在地不可长期预测。 　　混沌确定系统是庞加莱在研究三体问题时第一次发现的。-In nonlinear science, the "chaotic" and intended meaning of the word similar to but not exactly the same chaos in nonlinear science refers to a determined but not predictable state of motion. Its external performance and pure random motion is very similar to that are unpredictable. But the movement is different and random, chaotic motion is determined by the dynamics, and its unpredictability is derived from the movement of instability. Or chaotic systems an infinitesimal initial changes and also with the sensitivity of micro-wound, no matter how small perturbations in a long time after, but also make the system complete the evolution from the original direction. Chaos is a common phenomenon in nature, the weather is a typical chaotic motion. Chaos is one of the famous butterfly effect expression: a South American butterfly wings fan, it will cause a hurricane in Florida. Chaotic system has three key elements: First, the sensitive dependence on initial conditions　second, critical leve