Table 2 Comparison of the three conventions for a phase variable that we use in this review. The ϕ is used for IF models

ϑ

\(\mathbb {R}/T\mathbb {Z}\), [0,T)

\(\frac {\mathrm{d}}{\mathrm{d}t}\vartheta= 1\)

T

Simplicity of uncoupled equation, interpretation of ϑ as “time”

Phase space depends on parameters and initial conditions

θ

\(\mathbb {R}/2\pi \mathbb {Z}\), [0,2π)

\(\frac{\mathrm{d}}{\mathrm{d}t}\theta= \omega\)

\(\frac{2\pi}{\omega}\)

Phase space fixed, good for heterogeneous oscillators

Equation needs scaling

ϕ

\(\mathbb {R}/\mathbb {Z}\), [0,1)

\(\frac {\mathrm{d}}{\mathrm{d}t}\phi= \frac{1}{\Delta}\)

Δ

Phase space fixed, good for heterogeneous oscillators

Equation needs scaling