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Intralayer Synchronization in Evolving Multiplex Hypernetworks: Analytical Approach
SIAM Journal on Applied Dynamical Systems ( IF 1.7 ) Pub Date : 2020-04-23 , DOI: 10.1137/18m1224441
Sarbendu Rakshit , Bidesh K. Bera , Erik M. Bollt , Dibakar Ghosh

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 918-963, January 2020.
In this paper, we study intralayer synchronization of multiplex networks where nodes in each layer interact through diverse types of coupling functions associated with different time-varying network topologies, referred to as multiplex hypernetworks. Here, the intralayer connections are evolving with respect to time, and the interlayer connections are stagnant. In this context, an interesting and important problem is to analyze the stability of the intralayer synchronization in such temporal networks. We prove that if the dynamical multiplex hypernetwork for the time-average topology possesses intralayer synchronization, then each layer of the time-varying multiplex hypernetwork will also be synchronized for sufficiently fast switching. Then through master stability function formalism, we analytically derive necessary and sufficient stability conditions of intralayer synchronous states for such temporal architecture in terms of a time-average network. In this regard, we are able to decouple the transverse error component of the intralayer synchronization states for some special cases. Also, we extend our study for nonlinear intralayer coupling functions as well as multilayer hypernetwork architectures. Finally, the theoretical findings are verified numerically by taking the network of paradigmatic chaotic Rössler oscillators.


中文翻译:

不断发展的多重超网络中的层内同步:分析方法

SIAM应用动力系统杂志,第19卷,第2期,第918-963页,2020年1月。
在本文中,我们研究了多路复用网络的层内同步,其中每一层中的节点通过与不同时变网络拓扑相关联的各种类型的耦合功能进行交互,这些网络被称为多路复用超网络。这里,层内连接相对于时间在发展,并且层间连接是停滞的。在这种情况下,一个有趣且重要的问题是分析这种时间网络中层内同步的稳定性。我们证明,如果用于时均拓扑的动态多路复用超网络具有层内同步,那么时变多路复用超网络的每一层也将被同步以进行足够快速的切换。然后通过掌握稳定性函数形式主义,我们从时间平均网络的角度分析得出此类时间架构的层内同步状态的必要和充分稳定性条件。在这方面,对于某些特殊情况,我们能够解耦层内同步状态的横向误差分量。此外,我们扩展了对非线性层内耦合函数以及多层超网络体系结构的研究。最后,通过采用范式混沌Rössler振荡器网络对理论发现进行了数值验证。我们扩展了对非线性层内耦合函数以及多层超网络体系结构的研究。最后,通过采用范式混沌Rössler振荡器网络对理论发现进行了数值验证。我们扩展了对非线性层内耦合函数以及多层超网络体系结构的研究。最后,通过采用范式混沌Rössler振荡器网络对理论发现进行了数值验证。
更新日期:2020-06-30
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