Compositionality issues in discrete, continuous, and hybrid systems

Models of complex dynamical systems are often built by connecting submodels of smaller parts. The key to this method is the operation of 'interconnection' or 'composition' which serves to define the whole in terms of its parts. In the setting of smooth differential equations the composition operation has often been regarded as trivial, but a quite different attitude is found in the discrete domain where several definitions of composition have been proposed and different semantics have been developed. The non-triviality of composition carries over from discrete systems to hybrid systems. The paper discusses the compositionality issue in the context of discrete, continuous, and hybrid systems, mainly on the basis of a number of examples.