Abstract
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 5n equilibrium points located in $\Re^n$, and 3n 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.
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