Multistability of Recurrent Neural Networks With Nonmonotonic Activation Functions and Unbounded Time-Varying Delays

This paper is concerned with the coexistence of multiple equilibrium points and dynamical behaviors of recurrent neural networks with nonmonotonic activation functions and unbounded time-varying delays. Based on a state space partition by using the geometrical properties of the activation functions, it is revealed that an n-neuron neural network can exhibit Π_i=1ⁿ(2K_i + 1) equilibrium points with K_i ≥ 0. In particular, several sufficient criteria are proposed to ascertain the asymptotical stability of Π_i=1ⁿ(K_i + 1) equilibrium points for recurrent neural networks. These theoretical results cover both monostability and multistability. Furthermore, the attraction basins of asymptotically stable equilibrium points are estimated. It is shown that the attraction basins of the stable equilibrium points can be larger than their originally partitioned subsets. Finally, the results are illustrated by using the simulation results of four examples.