Evolving Dynamical Networks: a formalism for describing complex networks

We introduce a comprehensive formalism called an Evolving Dynamical Network (EDN) that aims to provide a common description for many types of complex system in applied science and engineering. We expand the currently available formalisms and define a new modeling framework able to incorporate network topology, dynamics, and evolution in an integrated way. Although the main focus is to provide a common framework, we find that evolving dynamical networks also highlight several interesting implications regarding possible control mechanisms for complex systems. A physical example is used throughout to illustrate the advantages and limitations of the various approaches described in the article.