两物种竞争系统演化与突进的相图分析

A Phase Analysis for the Advance and Catastrophe of a Competition System of Two Species

本文基于一般系统论中的相似性与同构性,用数学生态学的理论与方法,对社会经济系统中两种产业部门之间的竞争关系,及其演化与突进现象进行相图分析,证明了经济系统存在着由无序到有序演化的规律性。

This paper gives a direct deseription of the special competition system of two species by means of phase analysis, some examples are presented. Then, by discussing the number of intersection points of P(x, y)=0 and Q(x, y)=0 with respect to the general kolmogorov-type equation it Concludes that under the conditions established in [5], the intersection points are successively pairivise stable and nonstable equilibrium points. Therefore, it is possible to describe the phase diagram of the adrance and eatestrophe of the orbit-curves of the system via its field of gradients. Moreover this phase method can be used to tistify some related results in the theory of dissipative stracture and synergeties.