标题： 自适应振荡器网络中的同步簇爆发 显示英文标题

标题： Synchronization cluster bursting in adaptive oscillators networks

摘要： 自适应动态网络在现实世界系统中无处不在。 本文旨在探讨基于自适应耦合相位振子范式系统的自适应振子网络中的同步动力学。 我们的数值观察揭示了同步簇爆发的出现，其特征是在簇同步和全局同步之间周期性过渡。 通过研究一个简化模型，阐明了同步簇爆发的机制。 我们表明，可以将表现出这种现象的最小模型简化为具有复数值适应性的相位振子。 此外，系统的适应性导致了额外对称性的出现，从而导致具有非常不同的Kuramoto序参数的稳定爆发解共存。 显示英文摘要

摘要： 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.