Prefix orders as a general model of dynamics

In this report we formalize and study the notion of prex order on the executions of general dynamical systems and use basic category theory to show that appropriate structure preserving maps between such orders lead to the well-known notions of bisimulation, renement, product, and union of behavior, without relying on a notion of 'next state'. Thus these notions are generalized to apply to arbitrary dynamical systems, including continuous and hybrid systems.