The chimera states of phase oscillator populations with nonlocal higher-order couplings

Abstract

Abstract The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems. Here, we generalize the kuramoto model with nonlocal coupling incorporating the higher-order interactions encoded with the simplicial complexes. Previous works have shown that the higher-order interactions promote the coherent states. However, we uncover that the introduced higher-order couplings can significantly enhance the emergence of the incoherent state. Remarkably, we identify that the chimera states arise as a result of the multi-attractors in the dynamical states. Importantly, we review that the increasing higher-order interactions can significantly shape the emergent probability of chimera states. All the observed results can be well described in terms of the dimension reduction method. This study is a step forward in highlighting the importance of nonlocal higher-order couplings, which might provide control strategies for the occurrence of spatialtemporal patterns in networked systems.