Multistability of delayed recurrent neural networks with mexican hat activation functions

This letter studies the multistability analysis of delayed recurrent neural networks with Mexican hat activation function. Some sufficient conditions are obtained to ensure that an n-dimensional recurrent neural network can have 3^k15^k2 equilibrium points with 0≤k1 + k2≤n, and2^k13^k2 of them are locally exponentially stable. Furthermore, the attraction basins of these stable equilibrium points are estimated. We show that the attraction basins of these stable equilibrium points can be larger than their originally partitioned subsets. The results of this letter improve and extend the existing stability results in the literature. Finally, a numerical example containing different cases is given to illustrate the theoretical results.