5. Numerics confirm these rules across diverse oscillators F and coupling functions G:
7. The beauty of these rules is that they apply to interactions of any sizes, or mix of sizes.
And they tell us which phase models to use to represent a given nonlinear system, based on symmetry, without performing phase reduction.
6. These rules can be used as a design principle: by smoothly tuning the symmetry of a modified Stuart-Landau oscillator, we tune the resulting phase coupling functions.
