This article is devoted to discussing the exponential synchronization for a kind of delay derivative coupled neural networks with stochastic disturbance and multiple time-varying delays. To simulate more practical situations and widen the synchronization application fields in network science, the coupled neural networks with cluster-tree topology structure is studied by applying a novel impulsive pinning control strategy, which skillfully considered the neural networks in current cluster that directly linked to the neural networks in other clusters. Since the existence of delayed impulses, the general comparison principle for normal impulsive differential equations is efficiently extended. In view of the concept of average impulsive interval, the parameters classification discussion method and the mathematical induction method, some judgement conditions for achievement of the cluster synchronization on derivative coupled neural networks are derived. Additionally, the exponential convergence velocity of the derivative coupled neural networks is accurately estimated. Finally, numerical examples are presented to demonstrate the effectiveness of the control strategy and the theoretical results.

中文翻译：

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具有簇树拓扑结构的导数耦合神经网络的脉冲同步

本文致力于讨论一类具有随机扰动和多时变时滞的时滞导数耦合神经网络的指数同步问题。为了模拟更多的实际情况，拓宽网络科学中的同步应用领域，通过应用一种新颖的脉冲钉扎控制策略，巧妙地考虑了当前集群中直接链接的神经网络，研究了具有簇树拓扑结构的耦合神经网络。其他集群中的神经网络。由于延迟脉冲的存在，正规脉冲微分方程的一般比较原理得到了有效的扩展。针对平均脉冲区间的概念，参数分类讨论法和数学归纳法，推导出实现微分耦合神经网络集群同步的一些判断条件。此外，精确估计了导数耦合神经网络的指数收敛速度。最后，通过数值例子证明了控制策略的有效性和理论结果。