What is chaos theory? What is its application?

Chaos theory is a method combining qualitative thinking with quantitative analysis, which is used to discuss behaviors in dynamic systems (such as population movement, chemical reaction, meteorological change, social behavior, etc.). ) can only be explained and predicted by a whole and continuous data relationship. Chaos theory is a method with both qualitative thinking and quantitative analysis, which is used to discuss the behavior that cannot be explained and predicted by a single data relationship in a dynamic system, but must be explained and predicted by a whole and continuous data relationship. "The original state of everything is a pile of seemingly unrelated fragments, but after this chaotic state is over, these inorganic fragments will be organically integrated into a whole." The word chaos originally refers to the chaotic state before the formation of the universe. Ancient Greek philosophers held the chaos theory about the origin of the universe from the beginning of chaos, and thought that the universe gradually formed an orderly world today. In the orderly universe, western natural scientists have discovered many laws in nature one by one after a long discussion, such as gravity, lever principle, relativity and so on. These natural laws can be described by a single mathematical formula, according to which the behavior of objects can be accurately predicted. For nearly half a century, scientists have found that many natural phenomena can be simplified into simple mathematical formulas, but their behaviors are unpredictable. For example, meteorologist Edward Lorenz found that simple thermal convection can actually cause unimaginable meteorological changes, thus producing the so-called "butterfly effect". In 1960s, Stephen Smale, an American mathematician, found that after some regular changes, the subsequent development did not have a certain trajectory to follow, showing a state of disorder and chaos.