Phase chimera states on non-local hyperrings

Chimera states are dynamical states where regions of synchronous trajectoriescoexist with incoherent ones. A significant amount of research has been devotedto study chimera states in systems of identical oscillators, non-locallycoupled through pairwise interactions. Nevertheless, there is an increasingevidence, also supported by available data, that complex systems are composedby multiple units experiencing many-body interactions, that can be modeled byusing higher-order structures beyond the paradigm of classic pairwise networks.In this work we investigate whether phase chimera states appear in thisframework, by focusing on a novel topology solely involving many-body,non-local and non-regular interactions, hereby named non-local d-hyperring,being (d+1) the order of the interactions. We present the theory by using theparadigmatic Stuart-Landau oscillators as node dynamics, and show that phasechimera states emerge in a variety of structures and with different couplingfunctions. For comparison, we show that, when higher-order interactions are"flattened" to pairwise ones, the chimera behavior is weaker and more elusive.