平面C^2—动态系统平衡态的几何定性

The Geometric Qualitative Method of Equilibria of Planar C^2——Dynamical System

本文提出一个平面 C^2——动态系统几何定性相图的作法,改进并简化了以线性系统平衡态的非零代数特征值作为局部拓扑等价系统的平面定性分类的经典计算方法.文中引进一些直观显然的几何特征量,当系统结构稳定时,合理地用这些不精确的量直接观察它们作出的定性特征,可以与精确计算判定的结果一致.当结构不稳时也可以观察到临近不稳时定性性态的改变.用此方法能简化高次复杂的经典计算,直接从图中作出准确定性.本文提出的生物数学常微模型定性制图学的方法,属于生物数学的一个重要的发展方向.

This paper presents a geometric sketch of qualitative portrait of multi-equilibria of planar C^2-dynamical System which improve and simplify the classical method of calcula- tions with algebraic non-zero cigen values of equilibra of linear system as the qualitative classification of the local topological equivalent systens.In this paper we introduce some intutve trivially geometric characteristics,when the system is structurally stable,the direct watching their graphical qualitative portrait with imprecise but reasonable criterion which may be consistent with the result obtained from the precise calculations by classical meth- od.When the system is structurally unstable,we may also observe their variations of the qualitative behavior beyond the unstable situations.It is a creation of a new discipline pro- viding a method of fundamental sketch of qualitative nomography of the ordinary differential equations in biomathematic models,even though,this new discipline is seldom known by our International scientific and teconological workers and it is only studied in a low-key fashion at present stage but it shall be extended in an important developmental direction of the boundary science in biomathematics.