Energy Transmission and Synchronization in Complex Networks

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Focusing on the dynamics of energy transmission and distribution in power grids, this work explores the robustness of these systems under various modifications. It establishes explicit relationships between grid structure, optimal energy flow, and collective behavior, particularly synchronous power generation. Additionally, the thesis reviews network and spectral theory, offering analytical tools to analyze periodic behaviors in complex networks of phase oscillators, making it applicable to a range of complex systems beyond power grids.