This paper focuses on the global exponential synchronization of multiple memristive reaction-diffusion neural networks (MRDNNs) with time delay. Due to introducing the influences of space as well as time on state variables and replacing resistors with memristors in circuit realization, the state-dependent partial differential mathematical model of MRDNN is more general and realistic than traditional neural network model. Based on Lyapunov functional theory, Divergence theorem and inequality techniques, global exponential synchronization criteria of coupled delayed MRDNNs are derived via directed and undirected nonlinear coupling. Finally, three numerical simulation examples are presented to verify the feasibility of our main results.

中文翻译：

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耦合时滞忆阻反应扩散神经网络的全局同步。

本文着重研究具有时滞的多个忆阻反应扩散神经网络（MRDNN）的全局指数同步。由于引入了空间和时间对状态变量的影响，并且在电路实现中用忆阻器代替了电阻器，因此与传统的神经网络模型相比，MRDNN的状态相关偏微分数学模型更为通用和现实。基于Lyapunov泛函理论，发散定理和不等式技术，通过有向和无向非线性耦合，导出了耦合延迟MRDNN的全局指数同步准则。最后，给出了三个数值模拟实例，以验证我们的主要结果的可行性。