Improving synchronization with hypernetworks: Master stability function analysis and simulation validation

This work addresses the problem of improving synchronization quality in oscillator networks. To this end, the approach replaces some couplings involving one variable with couplings involving another, without increasing the total number of connections. When a network uses multiple coupling variables, it is referred to as a hypernetwork. The results include simulations of six different network topologies and three chaotic oscillators. Validation is performed through Monte Carlo simulations on the considered oscillator networks. A key finding is that using two coupling variables-while keeping the same number of connections as in a single-variable network and ensuring a fair scale for comparing coupling strengths-can significantly enhance synchronization quality.