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Network optimization strategies for the process of synchronization have generally focused on the re-wiring or re-weighting of links in order to: (1) expand the range of coupling strengths that achieve synchronization, (2) expand the basin of attraction for the synchronization manifold, or (3) lower the average time to synchronization. A new optimization goal is proposed in seeking the minimum subset of the edge set of the original network that enables the same essential ability to synchronize. We call this type of minimal spanning subgraph an Essential Synchronization Backbone (ESB) of the original system, and we present two algorithms for computing this subgraph. One is by an exhaustive search and the other is a method of approximation for this combinatorial problem. The solution spaces that result from different choices of dynamical systems and coupling vary with the level of hierarchical structure present and also the number of interwoven central cycles. These may provide insight into synchronization as a process of sharing and transferring information. Applications can include the important problem in civil engineering of power grid hardening, where new link creation may be costly, but instead, the defense of certain key links to the functional process may be prioritized.
Revealing how a biological network is organized to realize its function is one of the main topics in systems biology. The functional backbone network, defined as the primary structure of the biological network, is of great importance in maintaining t
In previously identified forms of remote synchronization between two nodes, the intermediate portion of the network connecting the two nodes is not synchronized with them but generally exhibits some coherent dynamics. Here we report on a network phen
In applications of dynamical systems, situations can arise where it is desired to predict the onset of synchronization as it can lead to characteristic and significant changes in the system performance and behaviors, for better or worse. In experimen
All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as networks
The features of animal population dynamics, for instance, flocking and migration, are often synchronized for survival under large-scale climate change or perceived threats. These coherent phenomena have been explained using synchronization models. Ho