Abstract In this paper, the finite-time synchronization problem for multi-coupling fuzzy cellular neural networks (FCNNs) with stochastic perturbations and mixed delays is addressed. Compared with exponential synchronization and asymptotic synchronization in existing literature, finite-time synchronization of stochastic FCNNs is studied for the first time, which is of better significance. Combining graph-theoretical technique and Lyapunov method, under the framework of feedback control, some finite-time synchronization conditions are derived. Besides, from the perspective of the connectedness of FCNNs, we just demand at least one directed path on the digraph between different vertices in networks, instead of each sub-network. Then, the convergence time is explicitly proposed, which is connected with the parameters of control and topological structure of networks. Eventually, a numerical example is also carried out to demonstrate the practicability and validity of our proposed results. Furthermore, a secure communication synchronization problem is presented to illustrate the effectiveness of the obtained results.

中文翻译：

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通过反馈控制的具有混合延迟的多耦合随机模糊神经网络的有限时间同步

摘要 在本文中，解决了具有随机扰动和混合延迟的多耦合模糊细胞神经网络 (FCNN) 的有限时间同步问题。与现有文献中的指数同步和渐近同步相比，首次研究了随机FCNNs的有限时间同步，具有更好的意义。结合图论技术和Lyapunov方法，在反馈控制的框架下，推导出一些有限时间同步条件。此外，从 FCNN 的连通性的角度来看，我们只要求网络中不同顶点之间的有向图上至少有一条有向路径，而不是每个子网络。然后，明确提出收敛时间，它与网络的控制参数和拓扑结构有关。最后，还进行了一个数值例子来证明我们提出的结果的实用性和有效性。此外，还提出了一个安全通信同步问题来说明所获得结果的有效性。