2次元区分線形微分方程式の挙動の定性解析 : (3) 大域解析アルゴリズムと例題

抄録

This paper concludes what is presented by previous two papers^^<(1)(2)>. The purpose of this paper is twofold: (a) to provide detailed description of the algorithm of global analysis for Topological Flow Analysis, a method of qualitative analysis of two dimensional piecewise linear differential equations, and (b) to provide the readers with an idea of how Topological Flow Analysis works as a whole, by illustrating a couple of concrete examples taken from experiments with a Common Lisp implementation of the theory. The paper presents two versions of the global analysis algorithm: one is faster but less powerful than the other. The basic idea underlying those algorithms is that global characteristic of phase portrait can be captured by examining the structure of orbits abstracted as mappings.