Chimera states in an adaptive higher-order network of Kuramoto oscillators

Many complex systems exhibit higher-order interactions, involving not just pairs but groups of units, that adapt over time in response to the system's dynamics. While previous studies on adaptive networks have primarily focused on pairwise interactions, the role of adaptive higher-order coupling in shaping emergent phenomena remains largely unexplored. In this work, we investigate the emergence of chimera states in nonlocally coupled Kuramoto oscillator networks featuring both first-order (pairwise) and second-order (triadic) interactions, where the coupling weights evolve adaptively. Using the mean local order parameter and the strength of incoherence as diagnostic tools, we systematically identify and characterize the parameter regions where chimera states occur. Our results show that when only first-order interactions are adaptive, the system supports a variety of dynamical states, including chimera states and cluster synchronization, depending on the phase-lag parameters. However, when second-order interactions are included, the region supporting chimera states becomes more restricted, and cluster synchronization disappears. This suppressive effect becomes more pronounced as the coupling strength of second-order interactions increases. These findings demonstrate that adaptive higher-order interactions play a critical role in modulating the stability and structure of chimera states, offering new insights into the interplay between topology, adaptivity, and non-pairwise dynamics in complex systems.