This paper is mainly concerned with the synchronization problem of reaction-diffusion neural networks (RDNNs) with delays and its direct application in image secure communications. An adaptive control is designed without a sign function in which the controller gain matrix is a function of time. The synchronization criteria are established for an error model derived from master-slave models through solving the set of linear matrix inequalities derived by constructing the suitable novel Lyapunov-Krasovskii functional candidate, Green's formula, and Wirtinger's inequality. If the proposed sufficient conditions are satisfied, then the global asymptotic synchronization of the error model is guaranteed. The numerical illustrations are provided to demonstrate the validity of the derived synchronization criteria. In addition, the role of system parameters is picturized through the chaotic nature of RDNNs and those unprecedented solutions is utilized to promote better security of image transactions. As is evident, the enhancement of image encryption algorithm is designed with two levels, namely, image watermarking and diffusion process. The contributions of this paper are discussed as concluding remarks.

中文翻译：

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反应自适应同步扩散神经网络及其在安全通信中的应用


本文主要研究带延迟的反应扩散神经网络（RDNN）的同步问题及其在图像保密通信中的直接应用。自适应控制的设计没有符号函数，其中控制器增益矩阵是时间的函数。通过构造合适的新型 Lyapunov-Krasovskii 函数候选、Green 公式和 Wirtinger 不等式来求解线性矩阵不等式组，从而为从主从模型导出的误差模型建立了同步准则。如果满足所提出的充分条件，则可以保证误差模型的全局渐近同步。提供的数值说明证明了导出的同步标准的有效性。此外，系统参数的作用通过 RDNN 的混沌性质来描绘，并且利用这些前所未有的解决方案来提高图像交易的安全性。可见，图像加密算法的增强设计分为两个层次，即图像水印和扩散处理。本文的贡献作为结论进行讨论。