异构延迟使父节点同步:Cayley树模型上的耦合映射

Aradhana Singh, S. Jalan
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引用次数: 1

摘要

研究了Cayley树网络上具有异构延迟值的扩散耦合映射中的相位同步簇。Cayley树网络由内部节点和边界节点两部分组成。我们发现异构延迟会导致不同的簇态,例如;(a)由内部节点和边界节点组成的集群状态;(b)仅由边界节点组成的集群状态。前一种状态可以由形成自组织集群的所有代的节点或根据异构延迟值的奇偶性产生驱动集群的少数代节点组成。此外,延迟的异质性破坏了边界上兄弟节点之间的精确同步,从而导致它们之间的滞后同步。时滞等于延迟值的差值。李亚普诺夫函数分析揭示了最后一代节点之间精确同步的破坏。最后,我们讨论了我们的结果与它们在家族企业中的应用以及在理解遗传疾病发生方面的相关性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Heterogeneous delays making parents synchronized: A coupled maps on Cayley tree model
We study the phase synchronized clusters in the diffusively coupled maps on the Cayley tree networks for heterogeneous delay values. Cayley tree networks comprise of two parts: the inner nodes and the boundary nodes. We find that heterogeneous delays lead to various cluster states, such as; (a) cluster state consisting of inner nodes and boundary nodes, and (b) cluster state consisting of only boundary nodes. The former state may comprise of nodes from all the generations forming self-organized cluster or nodes from few generations yielding driven clusters depending upon on the parity of heterogeneous delay values. Furthermore, heterogeneity in delays leads to the lag synchronization between the siblings lying on the boundary by destroying the exact synchronization among them. The time lag being equal to the difference in the delay values. The Lyapunov function analysis sheds light on the destruction of the exact synchrony among the last generation nodes. To the end we discuss the relevance of our results with respect to their applications in the family business as well as in understanding the occurrence of genetic diseases.
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