Local Assortativity Affects the Synchronizability of Scale-Free Network
Local Assortativity Affects the Synchronizability of Scale-Free Network
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DOI：
10.1109/jsyst.2022.3210408
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发表时间：
2021-11
影响因子：
4.4
通讯作者：
Mengbang Zou;Weisi Guo
中科院分区：
文献类型：
--
作者：
Mengbang Zou;Weisi Guo
同步对于物理、化学、生物和社会系统中的系统级行为至关重要。经验证据表明，网络拓扑结构强烈影响系统的同步性，分析它们之间的关系仍然是一个开放的挑战。我们知道特征值分布决定了网络的同步性，但是连接网络拓扑和所有相关特征值的解析表达式（例如，极值）仍然难以捉摸。在这里，我们准确地确定其同步性，提出了一种分析方法来估计极端的特征值，利用扰动理论。我们的分析方法揭示了全局和局部拓扑联合收割机的作用，影响同步性。我们发现，最小的非零特征值$\lambda ^{（2）}$，它确定同步性，估计由最小的程度增加了在最少的连接节点的程度差的倒数。由此，我们可以得出结论，$\lambda ^{（2）}$和具有最小度值的节点的局部可达性之间存在明显的负相关关系。我们在无标度网络的设置中验证了我们框架的准确性，并且可以由常用的常微分方程（例如，3-D Rosler动力学或Hindmarsh-Rose神经元回路）。从结果中，我们证明了网络的同步性可以通过重新连接这些特定节点的连接来调整，同时保持网络的一般度配置文件。
Synchronization is critical for system-level behavior in physical, chemical, biological, and social systems. Empirical evidence has shown that the network topology strongly impacts the synchronizability of the system, and the analysis of their relationship remains an open challenge. We know that the eigenvalue distribution determines a network's synchronizability, but analytical expressions that connect network topology and all relevant eigenvalues (e.g., the extreme values) remain elusive. Here, we accurately determine its synchronizability by proposing an analytical method to estimate the extreme eigenvalues using perturbation theory. Our analytical method exposes the role that global and local topology combine to influence synchronizability. We show that the smallest nonzero eigenvalue $\lambda ^{(2)}$, which determines synchronizability, is estimated by the smallest degree augmented by the inverse degree difference in the least connected nodes. From this, we can conclude that there exists a clear negative relationship between $\lambda ^{(2)}$ and the local assortativity of nodes with the smallest degree value. We validate the accuracy of our framework within the setting of a scale-free network and can be driven by commonly used ordinary differential equations (e.g., 3-D Rosler dynamics or Hindmarsh–Rose neuronal circuit). From the results, we demonstrate that the synchronizability of the network can be tuned by rewiring the connections of these particular nodes while maintaining the general degree profile of the network.