This paper focuses on the synchronization of fractional-order complex-valued neural networks (FOCVNNs) with reaction–diffusion terms in finite-time interval. Different from the existing complex-valued neural networks (CVNNs), the reaction–diffusion phenomena and fractional derivative are first considered into the system, meanwhile, the parameter switching (the system parameters will switch with the state) is considered, which makes the presented model more comprehensive. By choosing an appropriate Lyapunov function, the driver and response systems achieve Mittag-Leffler synchronization under a suitable controller. In addition, based on the fractional calculus theorem and the basic inequality methods, a criterion of synchronization for the error system in finite-time interval is derived and the upper bound of the corresponding finite synchronization time can be obtained. Finally, two examples are provided, one is a numerical example to explain the effectiveness of the main results, and the other shows that the results of this paper can be applied to image encryption for any size with high-security coefficient.

本文重点研究分数阶复值神经网络 (FOCVNN) 与有限时间间隔内的反应扩散项的同步。不同于现有的复值神经网络（CVNNs），系统首先考虑反应扩散现象和分数阶导数，同时考虑参数切换（系统参数会随着状态切换），这使得所提出的模型更全面。通过选择合适的 Lyapunov 函数，驱动器和响应系统在合适的控制器下实现 Mittag-Leffler 同步。此外，基于分数阶微积分定理和基本不等式方法，推导出误差系统在有限时间间隔内的同步判据，并得到相应有限同步时间的上界。最后给出了两个例子，一个是数值例子来说明主要结果的有效性，另一个表明本文的结果可以应用于任意大小的高安全系数图像加密。