IEEE Trans Neural Netw Learn Syst. 2012 Nov;23(11):1816-26. doi: 10.1109/TNNLS.2012.2210732.
In this paper, we are concerned with a class of neural networks with Mexican-hat-type activation functions. Due to the different structure from neural networks with saturated activation functions, a set of new sufficient conditions are presented to study the multistability, including the total number of equilibrium points, their locations, and stability. Furthermore, the attraction basins of stable equilibrium points are investigated for two-neuron neural networks. The investigation shows that the stable manifolds of unstable equilibrium points constitute the boundaries of attraction basins of stable equilibrium points. Several illustrative examples are given to verify the effectiveness of our results.
本文研究了一类具有墨西哥帽型激活函数的神经网络。由于与具有饱和激活函数的神经网络结构不同，文中提出了一组新的充分条件来研究多稳定性，包括平衡点的总数、位置和稳定性。此外，还研究了两个神经元神经网络稳定平衡点的吸引域。研究表明，不稳定平衡点的稳定流形构成了稳定平衡点吸引域的边界。给出了几个实例来说明我们结果的有效性。
