This article presents the design and implementation of a robust simulation methodology for hybrid models of physical systems that encompasses behavior patterns that undergo discrete transitions between modes of continuous behavior evolution. This methodology is based on a mathematical framework that captures time scale and parameter abstractions in modeling complex physical phenomena. The formal semantics for characterizing hybrid behaviors is defined in terms of three distinct modes of system operation: (1) continuous, (2) pinnacles, and (3) mythical. A key link is established between the switching transitions and the a priori and a posteriori state vector values, which defines the recursive mode switching functions that govern the interactions between the continuous and discrete components of the system models. The effectiveness of the approach is demonstrated by examples of physical system models that are presented along with a simulator to handle these.
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