Research on Basic Scientific Characters of Complexity, and Their Mathematics and Applications

Abstract

Based on the brief introduction of complexity, first we propose four basic scientific characters of complexity: much elements, various interactions, hierarchies, evolutions. Next, some corresponding mathematical methods of complexity are researched. Third, we discuss complexity in physics, and entropy is an important quantity. Fourth, nonlinearity of complexity is searched. Fifth, we research complexity in biology and neural networks. Finally, we study general sciences of complexity from chemistry, social sciences, to various applications. In a word, complexity is a complex science. Its investigations, developments and applications must be simplification and quantification.