Modeling of complex systems II: A minimalist and unified semantics for heterogeneous integrated systems

The purpose of this paper is to contribute to a unified formal framework for complex systems modeling. To this aim, we define a unified semantics for systems including integration operators. We consider complex systems as functional blackboxes (with internal states), whose structure and behaviors can be constructed through a recursive integration of heterogeneous components. We first introduce formal definitions of time (allowing to deal uniformly with both continuous and discrete times) and data (allowing to handle heterogeneous data), and introduce a generic synchronization mechanism for dataflows. We then define a system as a mathematical object characterized by coupled functional and states behaviors. This definition is expressive enough to capture the functional behavior of any real system with sequential transitions. We finally provide formal operators for integrating systems and show that they are consistent with the classical definitions of those operators on transfer functions which model real systems.