This paper studies a class of heterogeneous delayed impulsive neural networks with memristors and their collective evolution for multisynchronization. The multisynchronization represents a diversified collective behavior that is inspired by multitasking as well as observations of heterogeneity and hybridity arising from system models. In view of memristor, the memristor-based impulsive neural network is first represented by an impulsive differential inclusion. According to the memristive and impulsive mechanism, a fuzzy logic rule is introduced, and then, a new fuzzy hybrid impulsive and switching control method is presented correspondingly. It is shown that using the proposed fuzzy hybrid control scheme, multisynchronization of interconnected memristor-based impulsive neural networks can be guaranteed with a positive exponential convergence rate. The heterogeneity and hybridity in system models, thus, can be indicated by the obtained error thresholds that contribute to the multisynchronization. Numerical examples are presented and compared to demonstrate the effectiveness of the developed theoretical results.

中文翻译：

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具有模糊混合控制的基于互连忆阻器的脉冲神经网络的多重同步

本文研究了一类具有忆阻器的异构延迟脉冲神经网络及其多重同步的集体演化。多同步代表了一种多元化的集体行为，其灵感来自多任务处理以及对系统模型产生的异质性和混合性的观察。考虑到忆阻器，基于忆阻器的脉冲神经网络首先用脉冲微分包含来表示。根据忆阻和脉冲机理，引入了模糊逻辑规则，相应地提出了一种新的模糊混合脉冲和切换控制方法。结果表明，使用所提出的模糊混合控制方案，可以以正指数收敛速度保证基于互连忆阻器的脉冲神经网络的多重同步。因此，系统模型中的异质性和混合性可以通过获得的有助于多同步的误差阈值来表示。给出并比较了数值例子，以证明所开发的理论结果的有效性。