Chimera states on m-directed hypergraphs

TL;DR

This paper explores how non-reciprocal higher-order interactions in m-directed hypergraphs influence the emergence and characteristics of chimera states, revealing new phenomena not seen in reciprocal or pairwise systems.

Contribution

It demonstrates that directionality and higher-order interactions can induce chimera states, broadening understanding of their formation beyond reciprocal pairwise coupling.

Findings

Chimera states can emerge due to directionality in m-directed hypergraphs.

Higher-order interactions expand the parameter range for chimera occurrence.

Phase reduction theory validates the nature of phase chimeras.

Abstract

Chimera states are synchronization patterns in which coherent and incoherent regions coexist in systems of identical oscillators. This elusive phenomenon has attracted significant interest and has been widely analyzed, revealing several types of dynamical states. Most studies involve reciprocal pairwise couplings, where each oscillator exerts and receives the same interaction from neighboring ones, thus being modeled via symmetric networks. However, real-world systems often exhibit non-reciprocal, non-pairwise (many-body) interactions. Previous studies have shown that chimera states are more elusive in the presence of non-reciprocal pairwise interactions, while they are easier to observe when the interactions 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, which we compare with their corresponding networks, and we observe that some types of chimera states can emerge due to directionality, which had not been previously observed in its absence. We also compare the effect of non-reciprocal interactions between higher-order and pairwise couplings, and we find numerically that chimera states appear over a broader parameter range when considering higher-order interactions than in the corresponding network case, demonstrating the impact of directionality and the effect of higher-order interactions. Finally, the nature of phase chimeras has been further validated through phase reduction theory.