Chimera states on m-directed hypergraphs

Abstract: Chimera states are synchronization patterns in which coherent and incoherent regions coexist in systems of identical oscillators. This elusive phenomenon has attracted a lot of interest and has been widely studied, revealing several types of chimeras. Most cases involve reciprocal pairwise couplings, where each oscillator exerts and receives the same interaction, modeled via networks. However, real-world systems often have non-reciprocal, non-pairwise (many-body) interactions. From previous studies, it is known that chimera states are more elusive in the presence of non-reciprocal pairwise interactions, while easier to be found when the latter are reciprocal and higher-order (many-body). In this work, we investigate the emergence of chimera states on non-reciprocal higher-order structures, called m-directed hypergraphs, and we show that, not only the higher-order topology allows the emergence of chimera states despite the non-reciprocal coupling, but also that chimera states can emerge because of the directionality. Finally, we compare the latter results with the one resulting from non-reciprocal pairwise interactions: their elusiveness confirms that the observed phenomenon is thus due to the presence of higher-order interactions. The nature of phase chimeras has been further validated through phase reduction theory.