Stability in impulsive Cohen–Grossberg-type BAM neural networks with time-varying delays: A general analysis

Abstract

In this paper, we investigate a class of impulsive Cohen–Grossberg-type BAM neural networks with time-varying delays. By establishing the delay differential inequality with impulsive initial conditions, and employing the homeomorphism theory, the M-matrix theory and the inequality a ∏ k = 1 l b k q k ≤ ( 1 / r ) ( a r + ∑ k = 1 l q k b k r ) ( a ≥ 0 , b k ≥ 0 , q k ≥ 0 with ∑ k = 1 l q k = r − 1 , and r ≥ 1 ), some new sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive Cohen–Grossberg-type BAM neural networks with time-varying delays are derived. In particular, the estimate of the exponential convergence rate which depends on the system parameters and the impulsive disturbance intension is also provided. An example is given to show the effectiveness of the results obtained here.