Multistability of recurrent neural networks with time-varying delays and nonincreasing activation function

In this paper, we are concerned with a class of recurrent neural networks (RNNs) with nonincreasing activation function. First, based on the fixed point theorem, it is shown that under some conditions, such an n-dimensional neural network with nondecreasing activation function can have at least (4k+3)n equilibrium points. Then, it proves that there is only (4k+3)n equilibria under some conditions, among which (2k+2)n equilibria are locally stable. Besides, by analysis and study of RNNs with nondecreasing activation function, we can also obtain the same number of equilibria for RNNs with nonincreasing activation function. Finally, two simulation examples are given to show effectiveness of the obtained results.