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.

中文翻译：

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具有聚类树的耦合神经网络上基于矩阵测度的投影同步


本文主要研究具有混合时变延迟和簇树拓扑结构的非线性异构耦合神经网络阵列的投影准同步。针对参数不匹配和不同簇之间的相互影响的问题，研究了具有聚类树的耦合神经网络在规定误差范围内的指数准同步和全局准同步，而不是完全同步。设计了一种钉扎脉冲控制器，该控制器将在不同簇中的每个脉冲时刻将具有最大误差状态范数的神经网络强加于所选神经网络。利用平均脉冲间隔的概念、矩阵测度法和Lyapunov稳定性定理，推导了实现簇射影准同步的充分条件。同时，根据混合时变时滞脉冲系统的参数变化公式和比较原理，精确估计了收敛速度和同步误差界。此外，根据脉冲效应的不同函数，有效地优化了同步误差界限。最后通过数值实验验证了理论分析的结果。