Synchronization Cost of Coupled Oscillators With a Spatial Embedding

Synchronous behavior brings advantages for complex systems. Yet, this advantage comes with a cost: Emergence and sustainability of synchronization requires a continuous exchange among the interacting units. Thus, networks with optimal synchronization dynamics is a subject of active research. In this study, we define a cost function for synchronization which takes into account both the network structure which is embedded in space and the dynamic coupling within the system. Beginning from a fully connected network and using an edge pruning strategy based on simulated annealing, we searched for optimal configurations for synchronization with minimum cost. We observed that the same levels of synchronization with a fully connected network can be reached by different networks with sparse connections. We conclude that the chain structure, clustering behavior and degree-frequency relations are the main determinants of optimally synchronizable network structures.

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