一、什么是突变理论突变理论(Catastrophy Theory)作为一种新的数学理论,主要是由结构稳定性的拓扑概念发展过来的。1972年法国数学家Thom发表了开拓性的著作《结构稳定性和形态发生学》,系统地介绍了突变理论以及它在生物学,尤其是在动物胚胎学中的应用,在科学界引起巨大反响。后来有人不断将突变论的概念和方法引入物理学、力学、心理学、医学、社会学、经济学等领域。用数学模型来描写自然现象,是科学研究的一种基本方法。自从牛顿和莱布尼兹发明微积分 I. What is Catastrophy Theory? As a new mathematical theory, the Catastrophy Theory is mainly developed from the topological concept of structural stability. In 1972, the French mathematician Thom published a groundbreaking book “Structural stability and morphogenesis,” systematically describing the mutation theory and its application in biology, especially in animal embryology, and has caused great repercussions in the scientific community. . Later, people constantly introduced the concepts and methods of catastrophe theory into the fields of physics, mechanics, psychology, medicine, sociology, and economics. Using mathematical models to describe natural phenomena is a basic method of scientific research. Invented calculus since Newton and Leibniz