Finally, it should be pointed out that the essential significance of the extension of the Si'lnikov theorems is in helping to classify chaos in 3D autonomous polynomial systems, an interesting and yet challenging and long-standing problem in the mathematical chaos
You and Song ('Study on the chaos model of liquidity in the stock market') provide an elegant model of the process, and demonstrate how changes in the numbers of buyers, sellers and total traders can produce chaos (in the strict mathematical sense of the term--their graphs show this mathematical chaos
, and provide a warning that in certain conditions systems can become unmanageable.
This kind of mathematical chaos
is closely related to developments in complexity theory where small changes in the relation of simultaneously evolving processes interact to effect larger changes in the character of the entire system.
This unique creative process utilizes the mathematical equations of chaos theory to recreate images envisioned in the artist's "mind's eye." The color, structure and emotional content of each image is "painted" by Ralph using mathematical chaos