Reasoning about global behavior of ordinary differential equations by combining qualitative and quantitative analysis

The authors attempt to integrate numerical methods and knowledge-based methods with qualitative reasoning as a kernel. The essence of the approach is threefold: (a) representing geometric and topological aspects of solution curves relevant to qualitative analysis as mappings between hyperplanes in the phase space; (b) computing mappings that characterize the behavior by local analysis of solution curves; and (c) deriving global behaviors by analyzing structural information of the composite mappings representing solution curve. Preliminary results obtained from this approach are demonstrated for two-dimensional ordinary differential equations