循环-星形图案:网络对链接修改的响应

IF 2.6 2区 数学 Q1 MATHEMATICS, APPLIED Journal of Nonlinear Science Pub Date : 2024-05-06 DOI:10.1007/s00332-024-10034-6
Sajjad Bakrani, Narcicegi Kiran, Deniz Eroglu, Tiago Pereira
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引用次数: 0

摘要

了解如何进行有效修改以提高网络功能是科学界和工业界关心的一个基本问题。我们研究了弱连接有向图(由两个强连接部分组成:无向星形图和无向循环图)上的链路修改对网络动力学的影响。我们假设存在从循环开始到星形结束的有向边(主从形式)。我们通过添加任意大权重的有向边来修改图,这些有向边起始于星形,止于循环(切割集的相反方向)。我们提供的标准(基于星形和周期的大小、耦合结构以及切集和修改边的权重)决定了修改如何影响拉普拉斯矩阵的谱间隙。我们运用我们的方法来理解在混沌洛伦兹系统和罗斯勒系统网络中增强或阻碍同步的修改。我们的结果表明,链路添加对集体动力学的阻碍并不像之前的修正分析所预期的那样非典型,因此可以更好地控制集体特性。
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Cycle-Star Motifs: Network Response to Link Modifications

Understanding efficient modifications to improve network functionality is a fundamental problem of scientific and industrial interest. We study the response of network dynamics against link modifications on a weakly connected directed graph consisting of two strongly connected components: an undirected star and an undirected cycle. We assume that there are directed edges starting from the cycle and ending at the star (master–slave formalism). We modify the graph by adding directed edges of arbitrarily large weights starting from the star and ending at the cycle (opposite direction of the cutset). We provide criteria (based on the sizes of the star and cycle, the coupling structure, and the weights of cutset and modification edges) that determine how the modification affects the spectral gap of the Laplacian matrix. We apply our approach to understand the modifications that either enhance or hinder synchronization in networks of chaotic Lorenz systems as well as Rössler. Our results show that the hindrance of collective dynamics due to link additions is not atypical as previously anticipated by modification analysis and thus allows for better control of collective properties.

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来源期刊
CiteScore
5.00
自引率
3.30%
发文量
87
审稿时长
4.5 months
期刊介绍: The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. Papers should make an original contribution to at least one technical area and should in addition illuminate issues beyond that area''s boundaries. Even excellent papers in a narrow field of interest are not appropriate for the journal. Papers can be oriented toward theory, experimentation, algorithms, numerical simulations, or applications as long as the work is creative and sound. Excessively theoretical work in which the application to natural phenomena is not apparent (at least through similar techniques) or in which the development of fundamental methodologies is not present is probably not appropriate. In turn, papers oriented toward experimentation, numerical simulations, or applications must not simply report results without an indication of what a theoretical explanation might be. All papers should be submitted in English and must meet common standards of usage and grammar. In addition, because ours is a multidisciplinary subject, at minimum the introduction to the paper should be readable to a broad range of scientists and not only to specialists in the subject area. The scientific importance of the paper and its conclusions should be made clear in the introduction-this means that not only should the problem you study be presented, but its historical background, its relevance to science and technology, the specific phenomena it can be used to describe or investigate, and the outstanding open issues related to it should be explained. Failure to achieve this could disqualify the paper.
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