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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反应扩散神经网络的自适应同步及其在安全通信中的应用

本文主要关注具有时滞的反应扩散神经网络（RDNN）的同步问题及其在图像安全通信中的直接应用。设计了一种不带符号函数的自适应控制，其中控制器增益矩阵是时间的函数。通过解出线性矩阵不等式的集合，建立了从主从模型导出的误差模型的同步标准，该线性矩阵不等式是通过构造合适的新颖Lyapunov-Krasovskii函数候选，格林公式和维特林格不等式得出的。如果满足建议的充分条件，则可以保证误差模型的全局渐近同步。提供了数字说明以证明导出的同步标准的有效性。此外，系统参数的作用通过RDNN的混乱特性来描述，而那些空前的解决方案则用于促进更好的图像交易安全性。显而易见，图像加密算法的增强设计有两个层次，即图像水印和扩散过程。本文的结论作总结性讨论。