Abstractions and Realizations of Dynamic Networks

This paper establishes the importance of abstractions and realizations of dynamic networks in characterizing the structure and dynamics of systems. Abstractions and realizations generate dynamically equivalent representations of systems with varying degrees of structural detail. We show that dynamic networks exist that contain the same level of detail as state space models, that other dynamic networks exist that contain the same level of detail as transfer functions, and that still other dynamic networks exist that are simultaneously abstractions of state space models and realizations of transfer functions; thus containing intermediate levels of structural detail.