Automated analysis of qualitative behaviors of piecewise linear ordinary differential equations

One of the crucial issues in engineering problem solving is prediction of behavior, namely deriving the behavior from models. Prediction of behavior is not just calculation. Rather, it is an intellectual activity. High level decision making is needed to plan what and how to compute, monitor computation process, and interpret the result. Hence, a large portion of the prediction process has been indebted to human experts.As a first step towards this end, we concentrate on systems of piecewise linear ordinary differential equations (systems of PWL-ODEs), and proposeFlow Topology Analysis, a computational framework of analyzing systems of PWL-ODEs. We propose abstract representation, calledflow mappings, for describing qualitative aspects of solution curves in regions of the phase space. Flow mappings are used as an interface between knowledge and numerical levels. Currently, we have implemented the idea for systems of PWL-ODEs on two-dimensional phase spaces and partly for those on three-dimensional phase spaces.