Qualitative Analysis of Causal Feedback

Philippe Rose, Mark A. Kramer

An analysis of the properties of qualitative differential equations involving feedback structures is presented. The topological interpretation of this theory serves as the basis for a simulator of qualitative differential equations, QUAF. QUAF predicts the initial trend and final state of each variable, thereby elucidating the general character of the response. The approach requires that causal differential equations replace algebraic forms derived from pseudo-steady state (moving equilibrium) assumptions. QUAF is compared to the qualitative simulator QSIM on an example involving interconnected tanks, and a significant narrowing of the number of interpretations of system behavior is observed.

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