Multistability of Complex-Valued NNs With General Periodic-Type Activation Functions and Its Application to Associative Memories
研究了具有一般周期型激活函数的复值神经网络的多稳定性，通过引入该激活函数获得三种不同数量的平衡点，并分析了其存在性与稳定性，最后应用于联想记忆设计以提升存储容量。
This article mainly studies the multistability of complex-valued neural networks (CVNNs) with general periodic-type activation functions. In order to improve the storage capacity of associative memory, a general periodic-type activation function is introduced which obtains three different numbers of equilibrium points (EPs), including unique, finite, and countable infinite. The existence and stability of equilibria are investigated based on Brouwer’s fixed point theorem and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -matrix method. By means of a sign function on complex numbers, stability is confirmed using a new norm on the absolute values of the real and imaginary parts. The attraction basins of exponentially stable equilibria are estimated, which are bigger than the subspaces of the original division. Also, the design of associative memory is given. Finally, two numerical simulation examples verify the obtained results.