Studies on mathematical model for developmental systems

将生物发展形式化为数学系统是现代应用数学中最有趣的课题之一。作为生物发展的基础理论，这也是一部非常重要和有意义的著作。从这个角度出发，本研究项目取得了以下成果：(1)细胞分裂系统的图语法研究。通过将单元划分系统视为图语法，我们提出了路径控制图语法和协调语法。这些都是二维模式生成理论中富有成效的系统。(2)模糊概念的引入。将模糊概念引入发展系统是很自然的。为此，我们探究了模糊概念的一些基本性质，并取得了一些成果。(3)关于图论的一些成果。正如提到的一些地图生成系统。

It is one of the most interesting topics in modern applied mathematics to formalize biological developments as mathematical system. It is also a very important and significant work as the fundamantal theory of biological developments. From this point of view, we have obtained the following results in this research projent.(1) Graph-grammatical reseraxh of cell-division system. by considering cell-division systems as graph grammars, We have proposed path-controlled graph grammars and coordinated grammars. These are fruitful systems from the theory of two-dimensional pattern generations.(2) Introduction of fuzzy concept. It is natural to introduce fuzzy concept to developmental systems. To this end, we have pursued some fundamental properties of fuzzy concept and obtained some results.(3) Some results about graph theory. As mentioned some systems of map generations.