ABSTRACT
We investigate the impact of contrarians (via negative coupling) in multilayer networks of phase oscillators having higher-order interactions. We report that the multilayer framework facilitates synchronization onset in the negative pairwise coupling regime. The multilayering strength governs the onset of synchronization and the nature of the phase transition, whereas the higher-order interactions dictate the backward critical coupling. Specifically, the system does not synchronize below a critical value of the multilayering strength. The analytical calculations using the mean-field Ott-Antonsen approach agree with the simulations. The results presented here may be useful for understanding emergent behaviors in real-world complex systems with contrarians and higher-order interactions, such as the brain and social system.
ABSTRACT
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.
ABSTRACT
The presence of higher-order interactions (simplicial complexes) on globally coupled systems yield abrupt first-order transitions to synchronization. We discover that simplicial complexes on multilayer systems can yield multiple basins of attraction, leading to multiple abrupt first-order transitions to (de)synchronization for associated coupled dynamics. Using the Ott-Antonsen approach, we develop an analytical framework for simplicial complexes on multilayer systems, reducing the high-dimensional evolution equation to a low-dimensional manifold, which thoroughly explains the origin and stability of all possible dynamical states, including multiple synchronization transitions. The study illustrating rich dynamical behaviors could be pivotal in comprehending the impacts of higher-order interactions on dynamics of complex real-world networks, such as brain, social, and technological, which have inherent multilayer architectures.
