This paper concerns the multisynchronization issue for delayed fractional-order memristor-based neural networks with nonlinear coupling and almost-periodic perturbations. First, the coexistence of multiple equilibrium states for isolated subnetwork is analyzed. By means of state-space decomposition, fractional-order Halanay inequality and Caputo derivative properties, the novel algebraic sufficient conditions are derived to ensure that the addressed networks with arbitrary activation functions have multiple locally stable almost periodic orbits or equilibrium points. Then, based on the obtained multistability results, a pinning control strategy is designed to realize the multisynchronization of the $N$ coupled networks. By the aid of graph theory, depth first search method and pinning control law, some sufficient conditions are formulated such that the considered neural networks can possess multiple synchronization manifolds. Finally, the multistability and multisynchronization performance of the considered neural networks with different activation functions are illustrated by numerical examples.

本文涉及具有非线性耦合和几乎周期性扰动的基于延迟分数阶忆阻器的神经网络的多重同步问题。首先，分析了孤立子网多个平衡状态的共存问题。通过状态空间分解、分数阶 Halanay 不等式和 Caputo 导数性质，推导出新的代数充分条件，以确保具有任意激活函数的寻址网络具有多个局部稳定的近周期轨道或平衡点。然后，基于获得的多稳态结果，设计钉扎控制策略以实现多稳态同步。$N$耦合网络。借助图论、深度优先搜索方法和钉扎控制律，制定了一些充分条件，使得所考虑的神经网络可以拥有多个同步流形。最后，通过数值例子说明了所考虑的具有不同激活函数的神经网络的多稳定性和多同步性能。