A dynamic systems perspective on qualitative simulation

摘要

This paper presents a simple geometric interpretation of qualitative simulation (QS), based on the phase space representation of dynamic systems theory. QS consists of two steps: transition analysis determines the sequence of qualitative states that a system traverses and global interpretation derives its long-term behavior. I recast transition analysis as a search problem in phase space and replace the assorted transition rules with two algebraic conditions. The first condition determines transitions between arbitrarily shaped regions in phase space, as opposed to QS, which only handles n-dimensional rectangles. It also provides more accurate results by considering only the boundaries between regions. The second condition determines whether nearby trajectories approach a fixed point asymptotically. It obtains better results than QS by exploiting local stability properties. I recast global interpretation of dissipative systems as a search for attractors in phase space and present a global interpretation strategy for the subset of these systems whose local behavior determines global behavior uniquely. Although limited in scope, this strategy handles many systems that appear in the QS literature.