Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions

Abstract

Cohen-Grossberg neural networks with discontinuous activation functions is considered. Using the property of $M$-matrix and a generalized Lyapunov-like approach, the uniqueness is proved for state solutions and corresponding output solutions, and equilibrium point and corresponding output equilibrium point of considered neural networks. Meanwhile, global exponential stability of equilibrium point is obtained. Furthermore, by contraction mapping principle, the uniqueness and globally exponential stability of limit cycle are given. Finally, an example is given to illustrate the effectiveness of the obtained results.