Tiered synchronization in Kuramoto oscillators with adaptive higher-order interactions

Phase transitions widely occur in natural systems. Incorporation of higher-order interactions in coupled dynamics is known to cause first-order phase transition to synchronization in an otherwise smooth second-order in the presence of only pairwise interactions. Here, we discover that adaptation in higher-order interactions restores the second-order phase transition in the former setup and notably produces additional bifurcation referred as tiered synchronization as a consequence of combination of super-critical pitchfork and two saddle node bifurcations. The Ott-Antonsen manifold underlines the interplay of higher-order interactions and adaptation in instigating tiered synchronization, as well as provides complete description of all (un)stable states. These results would be important in comprehending dynamics of real-world systems with inherent higher-order interactions and adaptation through feedback coupling.

Automated summary

Phase transitions are common in natural systems. Incorporating higher-order interactions restores second-order phase transitions and generates tiered synchronization through a combination of super-critical pitchfork and two saddle node bifurcations. The Ott-Antonsen manifold provides a complete description of stable and unstable states and highlights the interplay between higher-order interactions and adaptation in instigating tiered synchronization. These findings are important for understanding the dynamics of real-world systems with inherent higher-order interactions and adaptation through feedback coupling.