This article is concerned with the exponential synchronization of coupled memristive neural networks (CMNNs) with multiple mismatched parameters and topology-based probability impulsive mechanism (TPIM) on time scales. To begin with, a novel model is designed by taking into account three types of mismatched parameters, including: 1) mismatched dimensions; 2) mismatched connection weights; and 3) mismatched time-varying delays. Then, the method of auxiliary-state variables is adopted to deal with the novel model, which implies that the presented novel model can not only use any isolated system (regard as a node) in the coupled system to synchronize the states of CMNNs but also can use an external node, that is, not affiliated to the coupled system to synchronize the states of CMNNs. Moreover, the TPIM is first proposed to efficiently schedule information transmission over the network, possibly subject to a series of nonideal factors. The novel control protocol is more robust against these nonideal factors than the traditional impulsive control mechanism. By means of the Lyapunov–Krasovskii functional, robust analysis approach, and some inequality processing techniques, exponential synchronization conditions unifying the continuous-time and discrete-time systems are derived on the framework of time scales. Finally, a numerical example is provided to illustrate the effectiveness of the main results.

中文翻译：

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时间尺度上具有基于拓扑的概率脉冲机制的耦合忆阻神经网络的多重不匹配同步

本文关注的是耦合忆阻神经网络 (CMNN) 在时间尺度上具有多个不匹配参数和基于拓扑的概率脉冲机制 (TPIM) 的指数同步。首先，通过考虑三种类型的不匹配参数来设计一个新模型，包括：1）不匹配的维度；2）不匹配的连接权重；3) 不匹配的时变延迟。然后，采用辅助状态变量的方法来处理新模型，这意味着所提出的新模型不仅可以使用耦合系统中的任何孤立系统（视为节点）来同步 CMNN 的状态，而且可以使用外部节点，即不隶属于耦合系统来同步 CMNN 的状态。而且，TPIM 最初是为了有效地调度网络上的信息传输而提出的，可能会受到一系列非理想因素的影响。新的控制协议比传统的脉冲控制机制更能抵抗这些非理想因素。通过Lyapunov-Krasovskii泛函、鲁棒分析方法和一些不等式处理技术，在时间尺度的框架上导出了统一连续时间和离散时间系统的指数同步条件。最后，给出了一个数值例子来说明主要结果的有效性。通过Lyapunov-Krasovskii泛函、鲁棒分析方法和一些不等式处理技术，在时间尺度的框架上导出了统一连续时间和离散时间系统的指数同步条件。最后，给出了一个数值例子来说明主要结果的有效性。通过Lyapunov-Krasovskii泛函、鲁棒分析方法和一些不等式处理技术，在时间尺度的框架上导出了统一连续时间和离散时间系统的指数同步条件。最后，给出了一个数值例子来说明主要结果的有效性。