Multistability of Memristive Neural Networks with Non-monotonic Piecewise Linear Activation Functions
Xiaobing Nie, Jinde Cao · Lecture notes in computer science · 2015
In this paper, a general class of non-monotonic piecewise linear activation functions is introduced and then the coexistence and dynamical behaviors of multiple equilibrium points are studied for a class of memristive neural networks (MNNs). It is proven that under some conditions, such n-neuron MNNs can have 5 n equilibrium points located in $\Re^n$ , and 3 n of them are locally exponentially stable, by means of fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis. The investigation shows that the neural networks with non-monotonic piecewise linear activation functions introduced in this paper can have greater storage capacity than the ones with Mexican-hat-type activation function.