Oscillatory and chaotic synchronization behavior in coupled oscillator systems with higher order interactions, community structure, and phase lags. 

Despite the prevalence of higher order interactions, phase lags, and community structure in many complex systems, their combined effects in synchronization processes remain unexplored. In this study, we consider coupled oscillator systems with higher order interactions mediated via hyperedges of size 2 (links) and size 3 (triangles), two communities, and identical phase lags between every interacting oscillator group. For some phase lags values, the system exhibits oscillatory and chaotic synchronization behavior, which is not present only when higher order interactions and community structure, or community structure and identical phase lags, are included. Some phase lag values result in almost synchronized and almost in-phase or almost anti-phase communities. For other phase lag values, we observe synchronized states with in-phase, anti-phase and skew phase communities, and incoherent-synchronized states. These results are supported by analytical equations derived using the Ott-Antonsen ansatz and numerical simulations.