Fig. 2: Emergent higher-order interactions from the original ring network.

Coupling functions appearing in Eq. (12) of node 1. Colors correspond to signs in the phase combination with blue standing for positive and orange for negative. a Resonant interaction term appearing as \({}^{2}{G}_{1}^{23}\). b Resonant interaction term appearing as \({}^{2}{G}_{1}^{43}\). Finally, c is a nonresonant term and d \({}^{2}{G}_{1}^{24}\) is a forbidden term (it does not appear). These new interaction terms can be predicted from the combinatorics of the original network and coupling function.