Anwar Md Sayeed, Rakshit Sarbendu, Kurths Jürgen, Ghosh Dibakar
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.
Department of Mechanical Engineering, University of California, Riverside, CA 92521, USA.
Entropy (Basel). 2023 Jul 19;25(7):1083. doi: 10.3390/e25071083.
Heterogeneity among interacting units plays an important role in numerous biological and man-made complex systems. While the impacts of heterogeneity on synchronization, in terms of structural mismatch of the layers in multiplex networks, has been studied thoroughly, its influence on intralayer synchronization, in terms of parameter mismatch among the layers, has not been adequately investigated. Here, we study the intralayer synchrony in multiplex networks, where the layers are different from one other, due to parameter mismatch in their local dynamics. In such a multiplex network, the intralayer coupling strength for the emergence of intralayer synchronization decreases upon the introduction of impurity among the layers, which is caused by a parameter mismatch in their local dynamics. Furthermore, the area of occurrence of intralayer synchronization also widens with increasing mismatch. We analytically derive a condition under which the intralayer synchronous solution exists, and we even sustain its stability. We also prove that, in spite of the mismatch among the layers, all the layers of the multiplex network synchronize simultaneously. Our results indicate that a multiplex network with mismatched layers can induce synchrony more easily than a multiplex network with identical layers.
相互作用单元之间的异质性在众多生物和人造复杂系统中起着重要作用。虽然已经深入研究了异质性在多重网络中层结构失配方面对同步的影响，但其在层间参数失配方面对层内同步的影响尚未得到充分研究。在这里，我们研究多重网络中的层内同步，其中由于各层局部动力学中的参数失配，各层彼此不同。在这样的多重网络中，引入层间杂质时，由于其局部动力学中的参数失配，层内同步出现的层内耦合强度会降低。此外，层内同步出现的区域也会随着失配的增加而扩大。我们通过分析得出了层内同步解存在的条件，甚至维持了其稳定性。我们还证明，尽管各层之间存在失配，但多重网络的所有层仍能同时同步。我们的结果表明，与各层相同的多重网络相比，层间失配的多重网络更容易诱导同步。
