Stability Analysis for a class of delayed neural networks with nonlinear homogeneous activation functions

The problem of asymptotic stability analysis is investigated about a class of delayed neural networks with homogeneous right-hands sides. Under the assumption that the trivial solution of delay free system is asymptotically stable and the activation functions are homogeneous, it is proved that the zero solution of delayed neural network is asymptotically stable for arbitrary nonnegative delay. By constructing a Lyapunov function and employing the nature of homogenous function, a new delay-independent asymptotically stability condition of the neural network with delay is obtained. At the end of the article, an appropriate numerical example which can demonstrate the effectiveness of the main result will be given.