Matrix Measure-Based Projective Synchronization on Coupled Neural Networks With Clustering Trees
研究了具有混合时变时滞和聚类树拓扑结构的异构耦合神经网络的投影准同步问题，设计了钉扎脉冲控制器，并给出了同步误差界和收敛速度的精确估计。
This article mainly studies the projective quasisynchronization for an array of nonlinear heterogeneous-coupled neural networks with mixed time-varying delays and a cluster-tree topology structure. For the sake of the mismatched parameters and the mutual influence among distinct clusters, the exponential and global quasisynchronization within a prescribed error bound instead of complete synchronization for the coupled neural networks with clustering trees is investigated. A kind of pinning impulsive controllers is designed, which will be imposed on the selected neural networks with some largest norms of error states at each impulsive instant in different clusters. By employing the concept of the average impulsive interval, the matrix measure method, and the Lyapunov stability theorem, sufficient conditions for the realization of the cluster projective quasisynchronization are derived. Meanwhile, in terms of the formula of variation of parameters and the comparison principle for the impulsive systems with mixed time-varying delays, the convergence rate and the synchronization error bound are precisely estimated. Furthermore, the synchronization error bound is efficiently optimized based on different functions of the impulsive effects. Finally, a numerical experiment is given to prove the results of theoretical analysis.