Complex Cluster States in Adaptive Network with High-Order Interaction

In this work, we study the influence of high-order interactions and coupling adaptivity on the dynamics of coupled oscillators. It was found that the introduction of second-order adaptive couplings leads to the emergence of a new type of synchronous behavior in the form of double antipodal clusters, which was not observed in the case of pairwise interactions. We also showed that oscillatory networks with combined high-order adaptive couplings can exhibit complex synchronous patterns, including multiclusters, chimeras and transient cluster states.