2024/09/12 by Mengke Wei, Andreas Amann, Wei, Mengke +9 · 1 citation
Computer Science · #Adaptation and Self-Organizing Systems (nlin.AO) #FOS: Physical sciences #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.2409.08348
openalex publication_date 2024/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Adaptive dynamical networks are ubiquitous in real-world systems. This paper aims to explore the synchronization dynamics in networks of adaptive oscillators based on a paradigmatic system of adaptively coupled phase oscillators. Our numerical observations reveal the emergence of synchronization cluster bursting, characterized by periodic transitions between cluster synchronization and global synchronization. By investigating a reduced model, the mechanisms underlying synchronization cluster bursting are clarified. We show that a minimal model exhibiting this phenomenon can be reduced to a phase oscillator with complex-valued adaptation. Furthermore, the adaptivity of the system leads to the appearance of additional symmetries and thus to the coexistence of stable bursting solutions with very different Kuramoto order parameters.