Dynamic and Topological Interplay in Adaptive Networks

Theory and applications of complex networks pervade nonlinear sciences. This chapter is devoted to adaptive networks which combine topological evolution of the network with dynamics in the network nodes – a property which yields a rich dynamical interplay between the state and the topology of the network. Recently, the dynamics of adaptive networks has been investigated in a number of parallel studies from different fields, ranging from genomics to game theory. Here we review these recent developments and show that they can be viewed from a unique angle. We demonstrate that all these studies are characterized by common themes – most prominently: complex dynamics and robust topological self-organization based on simple local rules. With our reviewwe aim to provide an overview of these central properties of adaptive networks, to outline the different perspectives fromwhich they have been considered and finally to set an agenda for future research.

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