Foundations of Networked Dynamical Systems
1. Introduction & Background From General Systems to Complex Networks The modern scientific worldview increasingly treats complex systems as networks of interacting components embedded in an environment. Whether describing power grids, ecosystems, economies, or neural tissue, these systems share a universal structure: Nodes represent dynamic states; edges represent interactions; and the network exists within a spatial, functional, or semantic environment that constrains and couples its evolution. This section formalizes the idea of a networked dynamical system (NDS); a graph endowed with both dynamics and spatial structure, and establishes the notation and conservation laws used throughout this book. Before doing so, it is useful to situate this concept within its intellectual lineage, tracing how modern network science grew from earlier efforts to describe feedback, control, and organization in complex systems. ...