An incorporation of higher-order interactions is known to lead an abrupt first-order transition to synchronization in otherwise smooth second-order one for pair-wise coupled systems. Here, we show that adaptation in higher-order coupling strength may yield completely different phenomena, notably, second-order transition to synchronization and tiered synchronization. Using the Ott-Antonsen approach, we perform rigorous theoretical calculations illustrating the origin of these emerging phenomena along with a complete description of all (un)stable states. Numerical simulations for limited-size networks are in agreement with the analytical predictions. These results would be important to comprehend dynamical behaviors of real-world complex systems with inherent higher-order interactions and adaptation through feedback coupling.
@article{arxiv.2302.12076,
title = {Tiered synchronization in adaptive Kuramoto oscillators on simplicial complexes},
author = {Priyanka Rajwani and Ayushi Suman and Sarika Jalan},
journal= {arXiv preprint arXiv:2302.12076},
year = {2023}
}