The limits of higher-order interactions in shaping chimera states

Abstract

In neuronal networks, chimera states, characterized by the coexistence of coherent and incoherent populations, have attracted considerable attention in the study of collective brain dynamics, due to its potential implications for neurological disorders such as epilepsy. Their emergence has been extensively investigated with a particular emphasis on the role of network topology, both in conventional pairwise interactions and, more recently, in higher-order interaction networks. Here, we propose a generalized framework for neuronal hypergraphs incorporating higher-order interactions through attractive chemical and repulsive electrical coupling. Using networks of FitzHugh--Nagumo neurons with interaction orders d=2,3,4, corresponding to (d+1)-body interactions within a framework that can be extended to higher d, we numerically investigate the emergence of chimera states under the combined effect of attractive and repulsive coupling and we compare the resulting dynamics with those of their corresponding clique-projected networks. Our results reveal that, both dynamical similarities and qualitative differences between genuine higher-order interactions on hypergraphs and their pairwise representations. While higher-order interactions often support broader chimera regions, we show that clique projections can also preserve or promote chimera states, even in regimes where the corresponding hypergraphs exhibit fully incoherent dynamics. Therefore, these findings suggest that chimera formation is not only influenced by the topology or by the interaction order but also by the form of the coupling functions and the balance between attractive and repulsive interactions, offering further insights into collective dynamics in neuronal networks.