高阶网络牵制控制中单纯形的选择

Selection of simplexes in pinning control of higher-order networks

随着网络科学的发展,普通网络无法描述多个个体间的交互作用,这就有必要引入高阶网络.高阶网络能够刻画普通网络无法描述的网络特征,其中单纯形(2阶以上)扮演着关键角色.牵制控制具有“四两拨千斤”的作用,在高阶网络中只需牵制一部分单纯形就能达到同步.但如何选取合适的单纯形进行牵制控制,是一个充满挑战而又全新的课题.本文给出高阶网络达到同步的自适应牵制控制律,并提出如何选择合适的单纯形进行牵制,选择方式由高阶网络广义Laplacian矩阵次小特征值对应的单位特征向量分量决定.数值仿真结果表明该方法简单有效,牵制控制效果与单纯形选择方式一致.

With the development of network science,simple networks have their limitations to capture interactions among multiple individuals.Therefore,it is significant to focus on the development of higher-order networks.Simplexes above 2 orders play a key role in higher-order networks,which can describe the network characteristics.In higher-order networks,pinning control is crucial as synchronization can only be attained by pinning certain simplexes.However,selecting proper simplexes for pinning control is a challenging and novel problem.The paper introduces an adaptive pinning control law designed to attain synchronization and a method for selecting suitable simplexes in higher-order networks.This method relies on the unit eigenvector component corresponding to the second smallest eigenvalue of the generalized Laplacian matrix associated with network topology.The results of the pinning control are consistent with that of selecting simplexes,and numerical simulations show the simplicity and effectiveness of this approach.