标题： 相位滞后对具有高阶相互作用的自适应多层网络同步的影响 显示英文标题

标题： Effect of phase-lag on synchronization in adaptive multilayer networks with higher-order interactions

摘要： 我们研究在相位挫折（$\beta$）存在的情况下，具有高阶相互作用的自适应多层网络中的同步过渡，既进行理论分析又进行数值模拟。 高阶拓扑结构包括成对和三元耦合。 研究的理论框架基于Ott-Antonsen假设，这导致了一个方便的低维模型。 对低维模型进行了广泛的分岔分析，并对完整网络进行了数值模拟，以探索同步路径。 综合分析表明，同步过渡对适应指数、耦合强度、相位滞后参数和多层配置有复杂的依赖关系。 系统在参数空间的不同区域表现出多种类型的同步过渡，即连续的、分层的和爆炸性的。 在所有情况下，都观察到低维模型与数值模拟结果之间良好的匹配。 通过低维模型可以清楚地理解不同同步过渡的起源。 对参数空间广阔区域的探索表明，相位挫折参数抑制了固定三元耦合强度下的疲劳以及爆炸性同步过渡（$K_2$）。 另一方面，对于固定的成对耦合强度（$K_1$），相位挫折参数促进了不连续的过渡。 此外，尽管在固定的$\beta$和$K_2$下高阶耦合占主导地位，但与成对耦合相关的适应函数的指数会减少滞回宽度。 而与高阶耦合相关的适应函数的指数则表现出相反的效果，在固定的$\beta$和$K_1$下，尽管成对耦合强度占主导地位，但它促进了双稳态。 显示英文摘要

摘要： We investigate the transition to synchronization in adaptive multilayer networks with higher-order interactions both analytically and numerically in the presence of phase frustration ($\beta$). The higher order topology consists of pairwise and triadic couplings. The analytical framework for the investigation is based on the Ott-Antonsen ansatz which leads to a convenient low-dimensional model. Extensive bifurcation analysis of the low-dimensional model and the numerical simulation of the full networks are performed to explore the paths to synchronization. The combined analysis shows a complex dependence of the transition to synchronization on adaptation exponents, coupling strengths, phase lag parameter, and multilayer configuration. Various types of transitions to synchronization, namely continuous, tiered, and explosive, are exhibited by the system in different regions of the parameter space. In all the cases, a satisfactory match between the low-dimensional model and the numerical simulation results is observed. The origin of different transitions to synchronization is clearly understood using the low-dimensional model. Exploration of a wide region of the parameter space suggests that the phase frustration parameter inhibits tired as well as explosive synchronization transitions for fixed triadic coupling strength ($K_2$). On the other hand, discontinuous transition is promoted by the phase frustration parameter for fixed pairwise coupling strength ($K_1$). Moreover, the exponent of the adaptation function with the pairwise coupling decreases the width of the hysteresis, despite the dominance of the higher-order coupling for fixed $\beta$ and $K_2$. While, the exponent of the function adapted with higher-order coupling shows the opposite effect, it promotes bistability in spite of dominance of pairwise coupling strength for fixed $\beta$, and $K_1$.