Local stability analysis of high-order recurrent neural networks with multi-step piecewise linear activation functions

In this paper, we investigate multistability for n-dimensional high-order recurrent neural networks with multistep piecewise linear activation functions. By Intermediate Value Theorem and definition of stability, sufficient criteria are derived for checking the existence of (r+1)ⁿ locally exponentially stable equilibria for high-order recurrent neural networks. And the attractive basins of locally exponentially stable equilibria are established. One numerical example is provided to demonstrate the effectiveness of the proposed stability criteria.