In a network of coupled oscillators, frequency heterogeneity — the oscillators running at different natural frequencies — typically destroys synchronization. The more different the frequencies, the harder it is to lock them together. This is the standard Kuramoto picture.

Add higher-order interactions (triadic coupling, where three oscillators influence each other simultaneously) and the picture inverts. Frequency heterogeneity substantially increases the global order parameter. The more different the frequencies, the more synchronized the system appears. Disorder promotes order.

But there’s a catch (arXiv:2603.14950). The same heterogeneity that expands the basin of attraction toward synchronized states simultaneously weakens the linear stability of those states. The system reaches order more easily but holds onto it less tightly. Heterogeneity is simultaneously the promoter of synchronization and the underminer of its robustness.

The through-claim: reaching a state and maintaining a state are different operations with different sensitivities. Heterogeneity makes it easier to fall into synchronization (larger basin of attraction) but harder to stay there (weaker linear stability). The two effects compete, creating a non-monotonic relationship between disorder and order. At moderate heterogeneity, the system is both more ordered and less stable than the homogeneous case — a combination that looks paradoxical only if you conflate arrival with persistence.