An Ontology for Transitions in Physical Dynamic Systems

Physical systems often exhibit complex nonlinear behaviors. To simplify behavioral analysis, we often introduce abstractions to hide details and more easily generate the dominant behaviors of a system. Given a system operating at multiple scales of time and space, we define equivalence relations over the set of system behaviors. Consequently, the entire domain of operation is partitioned into patches, called modes, with similar continuous behaviors. Discrete transitions move the system from one mode to another. Overall, subtle interactions between the continuous behaviors and discrete transitions require the development of a hybrid modeling and analysis paradigm. This paper presents a taxonomy of transitions and their accompanying modes: mythical, pinnacle, interior, boundary, and sliding behaviors, and synthesizes the transition conditions for the behaviors to develop a unified semantics and an efficient, self-consistent simulation algorithm for dynamic systems