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：

---

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同步的集体演化。多同步代表了一种多样化的集体行为，其灵感来自于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。从忆阻器的角度来看，基于忆阻器的脉冲神经网络首先以脉冲微分包含为代表。根据忆阻和脉冲机理，引入模糊逻辑规则，相应地提出了一种新的模糊混合脉冲和开关控制方法。结果表明，使用所提出的模糊混合控制方案，可以保证基于忆阻器的互连脉冲神经网络的多重同步，并具有正指数收敛率。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指示。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。