Comparative analysis
The important problem of predicting how a system reacts to perturbations in its parameters is discussed. The system means here a set of, in some sense, regular time functions (parameters) which are related through so called qualitative differential equations, i.e., ordinary differential equations obtained using differentiation, addition, multiplication and superposition of some monotonic functions on parameters as defined above. A novel technique is proposed, called differential qualitative analysis (DQ), within a framework of comparative analysis of dynamic systems which is based on many notions due to the qualitative simulation methodology. The original formal apparatus is developed which results in a basic set of propositions providing through formal reasoning (i.e. by application of general inference rules) a qualitative characterization of the system under study together with an explanation of its dynamic behavior. The notions essential to the reported theory such as that of parameter, landmark value, system, qualitative state, behavior, behavioral topology etc... are derived in common sense rather than in a rigorous mathematical style. But the least obvious propositions are formally proved. Two models not very far from reality are studied in a way to show the advantages of the DQ analysis and the limitations of the new technique. In particular perturbations changing the behavioral topology of the system are addressed in detail and some heuristics are proposed to overcome the difficulties. A computer program based on LISP for generating behaviors, performing a perturbation analysis of the chosen behavior and translating its results into assertions of the inference system, is described briefly. DQ is claimed to be incomplete in a sense explained in the paper. The suggestive and a bit esoteric formalism introduced in the paper contrasts with the simplicity of the models and situations considered.
scientific article; zbMATH DE number 4068691