Exponential stability and periodic solutions of delayed cellular neural networks

A set of criteria are presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov functionals. introducing many parameters q(ij)*, r(ij)*, q(ij), r(ij) is an element of R and w(i)>0 (i, j = 1, 2,..., n) and combining them with the elementary inequality 2 ab less than or equal to a(2) + b(2) technique. These criteria have important significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs. In addition, the results in literature are extended and improved. Two examples are given to illustrate the theory.