两类加权哑铃网络的一致性分析

Consensus Analysis of Two Types of Weighted Dumbbell Networks

网络的一致性是复杂网络科学的一个重要分支,其研究结果可以为理解网络的动力学行为提供理论依据。网络拓扑结构对网络一致性的鲁棒性有重要影响。文章首先根据经典的哑铃网络模型,分配边的权重,建立了符合实际应用的加权网络模型,其次结合网络一致性、图论等理论推导出加权网络的一阶和二阶一致性指标的具体解析式,进一步使用MATLAB软件数值模拟出两类哑铃网络的一致性指标对网络规模及耦合强度的依赖关系。研究结果表明,耦合强度的增大会使网络一致性增强,且节点全连接的哑铃网络具有更优的一阶与二阶一致性的鲁棒性。

The consensus of networks is an important branch of complex network science,and its research results can provide the theoretical basis for understanding the dynamic behavior of networks.The network topology has a significant impact on the robustness of network consensus.This article first assigns edge weights based on the classic dumbbell network model and establishes the weighted network model that is suitable for practical applications.Secondly,the specific analytical formulas of the first-order and second-order consistency indicators of the weighted network are derived by combining the theories of network consensus and graph theory.Furthermore,MATLAB software is used to numerically simulate the dependence of the consistency indicators of two types of dumbbell networks on network size and coupling strength.Finally,it is found that the increase in coupling strength leads to the increase in network consensus,and the dumbbell network with fully connected nodes has better robustness of first-order and second-order coherence.