Qualitative Analysis of Behavior of Two Dimensional Piecewise Linear Differential Equations : (2) Algorithm for Local Analysis

Abstract

In this paper and two other papers^^<(l)(2)>, we present Topological Flow Analysis, a method of qualitative analysis of two dimensional piecewise linear differential equations. The purpose of this paper is to present detailed description of an algorithm for local analysis, which implements the observation concerning local nature of two dimensional linear flow, obtained in the previous paper^^<(l)>. The algorithm presented here calls for only four arithmetic operations and square root to constrain local flow into finite number of possible interpretations. We have devised simple data structure called landmark orbit specification which enables to account geometric constraints as simple list manipulation.