In both examples, the introduction

In both examples, the introduction of higher-order in-teractions corresponds to having the state variable of anode influenced by a non-linear combination of the statesof several other nodes. Tuning the relative importance ofthe strength of the higher-order and pairwise interactionsprovides a way in both cases to change the nature of thetransition from continuous to discontinuous (Fig. 2c).The similarity of the mechanisms yielding a first-ordertransition in these two very different dynamical processesleads to conjecture that the introduction of non-linearhigher-order interactions and the tuning of their inten-sity is a general ingredient sufficient to provide abrupt transitions in a dynamical process.