Control of chimera states via adaptive higher-order interactions.

In recent years, adaptive higher-order interactions have garnered significant attention. However, most studies on chimera states in higher-order interaction networks have not considered coupling adaptation. In this work, we study a network of Kuramoto phase oscillators with first- and second-order interactions and adaptive couplings in two different network topologies: nonlocal and small-world. We show that, depending on the coupling strength, adaptation can induce a chimera state (where part of the network is synchronized, while the rest remains asynchronous) from a synchronous state or, conversely, synchronize a chimera state. Additionally, we find that small-world networks of Kuramoto phase oscillators exhibit a larger region of chimera states compared to nonlocal networks. Randomness of the topology realization plays an important role, and averaging over a number of realizations leads to increasing the possibility of a chimera state establishing. This work presents a novel approach to controlling the dynamics of adaptive higher-order interaction networks.