This paper presents the theoretical results on the multistability of state-dependent switching neural networks with discontinuous nonmonotonic piecewise linear activation functions. For n-neurons switching model, this paper shows that neural networks have 7ⁿ equilibrium points, 6ⁿ of which are located at the continuous points of activation functions and others are located at the discontinuous points of activation functions. Among these equilibrium points, 4ⁿ or 5ⁿ are stable and others are unstable, which depend on the relationship between the switching threshold and the discontinuous points of the activation functions. Compared with existing results, this paper reveals that switching threshold and discontinuous character are crucial in increasing the number of equilibrium points. Two examples are presented to verify the theoretical results.

本文介绍了具有不连续非单调分段线性激活函数的状态相关切换神经网络的多重稳定性的理论结果。对于n-神经元切换模型，本文表明神经网络具有7 ^n个平衡点，其中6 ^n个位于激活函数的连续点，其他的位于激活函数的不连续点。在这些平衡点中，4 ⁿ或5 ⁿ稳定和其他不稳定，这取决于切换阈值和激活函数的不连续点之间的关系。与现有结果相比，本文揭示了转换阈值和不连续特性对于增加平衡点的数量至关重要。给出两个例子来验证理论结果。