An Analysis of Complex-Valued Periodic Solution of a Delayed Discontinuous Neural Networks

Abstract

In this paper, we investigate global stability of complex-valued periodic solution of a delayed discontinuous neural networks. By employing discontinuous, nondecreasing and bounded properties of activation, we analyzed exponential stability of state trajectory and $L^1$−exponential convergence of output solution for complex-valued delayed networks. Meanwhile, we applied to complex-valued discontinuous neural networks with periodic coefficients. The new results depend on $M$−matrices of real and imaginary parts and hence can include ones of real-valued neural networks. An illustrative example is given to show the effectiveness of our theoretical results.