A new criterion for optimizing synchrony of coupled oscillators

Synchronization of coupled oscillators is important for understanding collective dynamics of a variety of natural and artificial systems including neuronal networks, Josephson junctions, and power grids. Despite this ubiquity, it remains unclear how the interaction between oscillator's dynamics and coupled structure either promotes or inhibits synchrony. Here, we introduce a Lyapunov function of the system such that it can be readily optimized to enhance synchrony of even heterogeneous oscillators on sparse networks. We consider two optimizing problems: frequency allocation and network design. Numerical experiments show that the proposed criterion outperform the promising methods, which is explained by a theoretical framework of the correlation between node degree and frequency magnitude.