Increase of

$a$

$d$

$N$

The case of synchronized region unbounded

$d<\frac{\text{2}a{\pi }^{\text{2}}}{N^2}$

${\lambda }_2\approx \text{2}d$

—

↑

—

$d>\frac{\text{2}a{\pi }^{\text{2}}}{N^2}$

${\lambda }_2\approx \frac{4a{\pi }^2}{N^2}$

↑

—

↓

The case of the synchronized region bounded

$d<\frac{\text{2}a{\pi }^{\text{2}}}{N^2}$

$R\approx \frac{a\left(\text{3}\pi +\text{2}\right)+\text{2}\pi d}{\text{2}\pi d}$

↓

↓

—

$d>\frac{\text{2}a{\pi }^{\text{2}}}{N^2}$

$R\approx \frac{a{N}^2\left(3\pi +2\right)+\text{2}\pi d{N}^2}{4a{\pi }^{\text{3}}}$

↓

↑

↑