Automated Phase Portrait Analysis by Integrating Qualitative and Quantitative Analysis

Toyoaki Nishida, Kenji Mizutani, Atsushi Kubota, Shuji Doshita

It has been widely believed that qualitative analysis guides quantitative analysis, while sufficient study has not been made from technical viewpoints. In this paper, we present a case study with PSX2NL, a program which autonomously analyzes the behavior of two-dimensional nonlinear differential equations, by integrating knowledge-based methods and numerical algorithms. PSX2NL focuses on geometric properties of solution curves of ordinary differential equations in the phase space. PSX2NL is designed based on a couple of novel ideas: (a) a set of flow mappings which is an abstract description of the behavior of solution curves, and (b) a flow grammar which specifies all possible patterns of solution curves, enabling PSX2NL to derive the most plausible interpretation when complete information is not available. We describe the algorithms for deriving flow mappings.

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