# How could we extend Kuramoto Model to Arbitrary Dimensions?

The generalised version of a theory describing synchronisation in an ensemble shows that coherence arises differently depending on whether the number of dimensions is even or odd. But how could you extend the Kuramoto model to arbitrary dimensions?

• The original Kuramoto model where each of the oscillators ($i=1 \cdots n$) phase ($\theta_{i}^{}$) coupled to other oscillators phases in the same way i.e., $\dot\theta_{i}^{}=\omega_{i}^{}+\frac{g}{n}\sum_{j=1}^{n}\sin[\theta_{i}^{}-\theta_{j}^{}]$ doesn't carry any information of dimensionality as it should be clear. Did you mean some variant of form for example, $\dot\theta_{i}^{}=\omega_{i}^{}+\sum_{\text{conditional}(j,i)}^{}g_{ij}^{}\sin[\theta_{i}^{}-\theta_{j}^{}]$ defined on some lattice (which certainly has dimensionality aspect). – Sunyam Jan 10 at 14:17