发表机构
National Institute of Technology, Durgapur（印度杜尔加布尔国家技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过Ott-Antonsen约化分析适应性双层Kuramoto网络，发现相位滞后不对称性导致双重爆炸性转变，产生八个同步状态，并验证了约化模型的准确性。
AI 中文摘要
两个相互作用的网络之间的不对称性能否从根本上改变它们的同步方式？我们在具有成对和三体相互作用以及不对称相位滞后的Kuramoto振荡器的适应性双层多路复用网络中，识别出前向方向、后向方向或两者组合中的双重爆炸性转变，并伴有单重或双重迟滞回线。利用Ott-Antonsen约化，我们推导出一个低维系统并进行稳定性分析。约化模型准确捕捉了完整的微观动力学，并为分岔点提供了解析表达式。跨多个参数平面的系统映射揭示了八种不同的同步状态。鞍结分岔点和音叉分岔点的相对顺序——由相位滞后不对称性、跨层适应性和高阶相互作用强度控制——产生了两个不同的相干分支（弱和强），从而引发双重爆炸性转变。关键的是，相位滞后不对称性作为一个稳健的控制旋钮：虽然对称的相位滞后抑制爆炸性转变，但层特异性差异促进多稳定性和双重爆炸性转变。高阶相互作用强度$K_2$以及适应性强度$q$、$p$和$h$进一步以复杂的、参数依赖的方式调节这些转变。解析预测与数值模拟之间的极好一致性证实了我们约化描述的稳健性。
英文摘要
Can asymmetry between two interacting networks fundamentally change how they synchronize? We identify double explosive transitions in the forward direction, backward direction, or a combination thereof, with single or double hysteresis loops in an adaptive bilayer multiplex network of Kuramoto oscillators with pairwise and three-body interactions and asymmetric phase lags. Using the Ott-Antonsen reduction, we derive a low-dimensional system and perform a stability analysis. The reduced model accurately captures the full microscopic dynamics and enables analytical expressions for the bifurcation points. Systematic mapping across multiple parameter planes reveals eight distinct synchronization regimes. The relative ordering of saddle-node and pitchfork bifurcation points---controlled by phase-lag asymmetry, cross-layer adaptation, and the higher-order interaction strength---creates two distinct coherent branches (weak and strong), giving rise to double explosive transitions. Crucially, phase-lag asymmetry acts as a robust control knob: while symmetric phase lags suppress explosive transitions, layer-specific differences promote multistability and double explosive transitions. The higher-order interaction strength $K_2$ and adaptation strengths $q$, $p$, and $h$ further modulate these transitions in a complex, parameter-dependent manner. Excellent agreement between analytical predictions and numerical simulations confirms the robustness of our reduced description.
Comments14 pages, 14 figures
