Multistability of Recurrent Neural Networks With Nonmonotonic Activation Functions and Mixed Time Delays

This paper presents new theoretical results on the multistability analysis of a class of recurrent neural networks with nonmonotonic activation functions and mixed time delays. Several sufficient conditions are derived for ascertaining the existence of 3
ⁿ
equilibrium points and the exponential stability of 2
ⁿ
equilibrium points via state space partition by using the geometrical properties of activation functions and algebraic properties of nonsingular M-matrix. Compared with existing results, the conditions herein are much more computable with one order less linear matrix inequalities. Furthermore, the attraction basins of these exponentially stable equilibrium points are estimated. It is revealed that the attraction basins of the 2
ⁿ
equilibrium points can be larger than their originally partitioned subspaces. Three numerical examples are elaborated with typical nonmonotonic activation functions to substantiate the efficacy and characteristics of the theoretical results.