Fig. 14

a A phase interaction given by \(\epsilon H(\theta) = \theta (\pi-\theta)(\theta-2 \pi)\) for \(\theta\in[0,2\pi)\) with complex Fourier series coefficients given by \(H_{n}=6i/n^{3}\). The remaining panels show the effect of flipping the sign of just one of the coefficients, namely \(H_{m} \rightarrow-H_{m}\). b \(m=1\), and the asynchronous solution will destabilise in favour of the synchronous solution since \(H'(0)>0\). c \(m=2\), and the asynchronous solution will destabilise in favour of a two-cluster. d \(m=3\), and the asynchronous solution will destabilise in favour of a three-cluster. Note that only small changes in the shape of H, as seen in panels c–d, can lead to a large change in the emergent network dynamics