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Networks of coupled time-delay digital tanlock loops: chimeras and other emergent spatiotemporal dynamics
Nonlinear Dynamics ( IF 5.6 ) Pub Date : 2020-09-09 , DOI: 10.1007/s11071-020-05918-7
Bishwajit Paul , Tanmoy Banerjee

Phase-locked loops are important engineering systems that are widely used in electronic communication systems. Although, in almost all the engineering applications they operate in coupled conditions; however, most of the studies explored their dynamics in the isolated condition. In this paper, we explore in detail the collective dynamics of a network of coupled time-delay digital tanlock loops (TDTLs). Both one- and two-dimensional networks of TDTLs with nonlocal coupling are studied in this paper. We carry out detailed stability analysis for the one-dimensional network and determine the stable zone of operation. We explore the appearance of exotic spatiotemporal patterns like chimeras and solitary states. For the two-dimensional network, a variety of chimera patterns, e.g., spot, linear stripe, wavy stripe, and inverted spot chimeras, are reported. We also identify the occurrence of breathing spot chimeras in two-dimensional network. We corroborate our results by characterizing the chimeras by proper measures in both one- and two-dimensional cases.



中文翻译:

耦合的延时数字tanlock环网络:嵌合体和其他新兴时空动力学

锁相环是重要的工程系统,广泛用于电子通信系统中。尽管,在几乎所有工程应用中,它们都是在耦合条件下运行的;但是,大多数研究在孤立条件下探索了它们的动力学。在本文中,我们将详细探讨耦合时延数字tanlock环路(TDTL)网络的集体动力学。本文研究了具有非局部耦合的TDTL的一维和二维网络。我们对一维网络进行详细的稳定性分析,并确定操作的稳定区域。我们探索异国时空模式的出现,例如嵌合体和孤立状态。对于二维网络,各种嵌合体模式,例如斑点,线性条纹,波浪条纹和倒置斑点嵌合体,被报道。我们还确定了二维网络中呼吸点嵌合体的发生。我们通过在一维和二维情况下通过适当的措施对嵌合体进行表征来证实我们的结果。

更新日期:2020-09-10
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