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

From: Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience

Symbol Phase space Uncoupled equation Period Advantages Disadvantages
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