Studies on mathematical model for developmental systems

将生物学的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。作为生物学发展的基础理论，它也是一项非常重要和有意义的工作.从这一角度出发，本研究项目取得了以下成果。(1)细胞分裂系统的图形语法研究。把单元划分系统看作是图文法，我们提出了路径控制图文法和协调文法。这些都是从二维图案生成理论出发的富有成果的系统。(2)引入模糊概念。将模糊概念引入开发系统是很自然的。为此，我们研究了模糊概念的一些基本性质，并得到了一些结果。(3)关于图论的一些结果。如前所述，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.