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。从这个角度来看，我们在这个研究项目中获得了以下结果。(1)细胞分裂系统的图语法研究。将细胞分裂系统视为图语法，提出了路径控制图语法和协调语法。这些都是二维图形生成理论中卓有成效的系统。(2)模糊概念的引入。在发展系统中引入模糊概念是很自然的。为此，我们对模糊概念的一些基本性质进行了探讨，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.