Controlling edge dynamics in complex networks

The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Here we introduce and evaluate a dynamical process defined on the edges of a network, and demonstrate that the controllability properties of this process significantly differ from simple nodal dynamics. Evaluation of real-world networks indicates that most of them are more controllable than their randomized counterparts. We also find that transcriptional regulatory networks are particularly easy to control. Analytic calculations show that networks with scale-free degree distributions have better controllability properties than uncorrelated networks, and positively correlated in- and out-degrees enhance the controllability of the proposed dynamics.Comment: Preprint. 24 pages, 4 figures, 2 tables. Source code available at http://github.com/ntamas/netctr

Resilience and Controllability of Dynamic Collective Behaviors

The network paradigm is used to gain insight into the structural root causes of the resilience of consensus in dynamic collective behaviors, and to analyze the controllability of the swarm dynamics. Here we devise the dynamic signaling network which is the information transfer channel underpinning the swarm dynamics of the directed interagent connectivity based on a topological neighborhood of interactions. The study of the connectedness of the swarm signaling network reveals the profound relationship between group size and number of interacting neighbors, which is found to be in good agreement with field observations on flock of starlings [Ballerini et al. (2008) Proc. Natl. Acad. Sci. USA, 105: 1232]. Using a dynamical model, we generate dynamic collective behaviors enabling us to uncover that the swarm signaling network is a homogeneous clustered small-world network, thus facilitating emergent outcomes if connectedness is maintained. Resilience of the emergent consensus is tested by introducing exogenous environmental noise, which ultimately stresses how deeply intertwined are the swarm dynamics in the physical and network spaces. The availability of the signaling network allows us to analytically establish for the first time the number of driver agents necessary to fully control the swarm dynamics

Structural Completeness of a Multi-channel Linear System with Dependent Parameters

It is well known that the "fixed spectrum" {i.e., the set of fixed modes} of a multi-channel linear system plays a central role in the stabilization of such a system with decentralized control. A parameterized multi-channel linear system is said to be "structurally complete" if it has no fixed spectrum for almost all parameter values. Necessary and sufficient algebraic conditions are presented for a multi-channel linear system with dependent parameters to be structurally complete. An equivalent graphical condition is also given for a certain type of parameterization