Global attractivity of Cohen–Grossberg model with finite and infinite delays

In this paper, we have studied the global attractivity of the equilibrium of Cohen–Grossberg model with both finite and infinite delays. Criteria for global attractivity are also derived by means of Lyapunov functionals. As a corollary, we show that if the delayed system is dissipative and the coefficient matrix is VL-stable, then the global attractivity of the unique equilibrium is maintained provided the delays are small. Estimates on the allowable sizes of delays are also given. Applications to the Hopfield neural networks with discrete delays are included.