Unique superdiffusion induced by directionality in multiplex networks
Unique superdiffusion induced by directionality in multiplex networks
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DOI：
10.1088/1367-2630/abdb71
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发表时间：
2020-11
影响因子：
3.3
通讯作者：
Xiangrong Wang;A. Tejedor;Yi Wang;Y. Moreno
中科院分区：
文献类型：
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作者：
Xiangrong Wang;A. Tejedor;Yi Wang;Y. Moreno
多层网络框架已经用来描述和揭示一些新的和不可预见的物理行为和相互作用的复杂系统的制度。然而，大多数现有的研究是建立在无向多层网络，而大多数复杂的系统在自然界中表现出定向相互作用。在这里，我们提出了一个框架来分析扩散动力学的多层网络组成的至少一个有向层。我们严格证明了多层网络中的方向性可以从根本上改变扩散动力学的行为：从单调（无向系统）到非单调扩散层间耦合强度。此外，对于某些多层网络配置，方向性可以诱导一个独特的超扩散制度的中间值的层间耦合，其中的扩散甚至比对应于无向系统的理论极限，即从每个层的聚集获得的集成网络中的扩散更快。我们从理论上和数值计算表明，超扩散的存在是完全由每一层的方向性和层之间的拓扑重叠。我们进一步提供了一个配方的多层网络显示超扩散。我们的研究结果突出了将相互作用的方向性在多级网络系统中的意义，并提供了一个框架，以分析相互关联的复杂系统的动力学过程的方向性。
The multilayer network framework has served to describe and uncover a number of novel and unforeseen physical behaviors and regimes in interacting complex systems. However, the majority of existing studies are built on undirected multilayer networks while most complex systems in nature exhibit directed interactions. Here, we propose a framework to analyze diffusive dynamics on multilayer networks consisting of at least one directed layer. We rigorously demonstrate that directionality in multilayer networks can fundamentally change the behavior of diffusive dynamics: from monotonic (in undirected systems) to non-monotonic diffusion with respect to the interlayer coupling strength. Moreover, for certain multilayer network configurations, the directionality can induce a unique superdiffusion regime for intermediate values of the interlayer coupling, wherein the diffusion is even faster than that corresponding to the theoretical limit for undirected systems, i.e. the diffusion in the integrated network obtained from the aggregation of each layer. We theoretically and numerically show that the existence of superdiffusion is fully determined by the directionality of each layer and the topological overlap between layers. We further provide a formulation of multilayer networks displaying superdiffusion. Our results highlight the significance of incorporating the interacting directionality in multilevel networked systems and provide a framework to analyze dynamical processes on interconnected complex systems with directionality.