Chaos theory (chaos theory)

The 20021Nobel Prize in Physics was awarded to two famous Japanese-American meteorologists, Shuro Makoto and Klaus Hasselman, in recognition of their "physical modeling of the earth's climate, quantification of its variability and reliable prediction of global warming".

Official website, the Nobel Prize winner, explained that all complex systems are made up of many different parts that interact with each other. Physicists have been studying them for centuries, and they are difficult to describe mathematically-there may be many components in the system, or they may be dominated by accidental factors. Complex systems may also be chaotic, such as weather, and small deviation of initial value will lead to big difference in later period. This year's winners have all contributed to gaining more knowledge about such systems and their long-term development.

With the development of science and people's in-depth understanding of the world, chaos theory is increasingly regarded as an important theory of complex systems, and its wide application in various industries is gradually favored by people.

1. Chaos theory is a branch of mathematics, which mainly studies the chaotic state of dynamic systems. The so-called chaotic state is actually a seemingly random phenomenon produced by a certain rule. Chaos and order coexist in a complex system.

1) The chaotic system looks chaotic because it is very sensitive to the initial error, which makes it impossible to accurately predict the long-term behavior of the chaotic system.

2) The mechanism of initial sensitivity lies in the existence of nonlinear interaction.

Nonlinear system is a system in which the change of output is not proportional to the change of input. The biggest difference between nonlinear system and linear system is that nonlinear system may lead to chaotic, unpredictable or intuitive results.

Nonlinear example: population growth curve

Butterfly effect is one of the most famous chaotic effects, which describes how a small change in a deterministic nonlinear state leads to a huge difference in a later state (meaning a sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in the Amazon River in South America can cause a hurricane in Texas in North America.