使双亲同步的异质时滞：Cayley树模型上的一个耦合映射
Heterogeneous delays making parents synchronized: A coupled maps on Cayley tree model
摘要：
本文研究了非均匀时延下Cayley树网络上扩散耦合映射中的相位同步簇。凯莱树网络由两部分组成：内部节点和边界节点。我们发现，异构延迟导致各种集群状态，如：（a）集群状态由内部节点和边界节点，和（b）集群状态仅由边界节点。前一种状态可以包括来自形成自组织集群的所有代的节点或来自产生驱动集群的少数代的节点，这取决于异构延迟值的奇偶性。此外，延迟的异质性通过破坏它们之间的精确同步而导致位于边界上的兄弟姐妹之间的滞后同步。时间滞后等于延迟值的差。李雅普诺夫函数分析揭示了破坏的最后一代节点之间的精确同步。最后，我们讨论了我们的研究结果的相关性，他们在家族企业中的应用，以及在了解遗传疾病的发生。
英文摘要：
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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