In this paper, time-varying and distributed delays are introduced into competitive neural networks and the global exponential stability for the neural networks is investigated. By using this analysis method, inequality techniques, and the properties of an M-matrix, several novel delay-independent sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the equilibrium point are derived. The obtained results are different from and less restrictive than those given in the existing literature, and the boundedness and differentiability of the activation functions and the differentiability of the time-varying delays are removed. Two examples with their simulations are given to show their good agreement with the theoretical results.
EngelP. M.MolzR. F.A new proposal for implementation of competitive neural networks in analog hardware. In Proceedings of the Fifth Brazilian Symposium on Neural networks, Belo Horizonte, Brazil, 1998, pp. 186–191 (IEEE Press, New York).
2.
Meyer-BaeseA.OhlF.ScheichH.Singular perturbation analysis of competitive neural networks with different timescales. Neural Comput., 1996, 8, 1731–1742.
3.
Meyer-BaeseA.PilyuginS.ChenY.Global exponential stability of competitive neural networks with different time scales. IEEE Trans. Neural Networks, 2003, 14(3), 716–719.
4.
Meyer-BaeseA.PilyuginS.WismullerA.FooS.Local exponential stability of competitive neural networks with different time scales. Engng Appl. Artif. Intell., 2004, 17, 227–232.
5.
MaoY.Multistability of competitive neural networks with different time scales. In Proceedings of the International Conference on Communications, circuits and systems, Hong Kong, 2005, pp. 939–943 (IEEE Press, New York).
6.
LuH.Shun-ichiA.Global exponential stability of multitime scale competitive neural networks with nonsmooth functions. IEEE Trans. Neural Networks, 2006, 17(5), 1152–1164.
7.
LuH.HeZ.Global exponential stability of delayed competitive neural networks with different time scales. Neural Networks, 2005, 18, 243–250.
8.
MarcussC. M.WesterveltR. M.Stability of analog neural networks with delay. Phys. Rev. A., 1989, 39(1), 347–359.
HuangX.CaoJ.HoD. W. C.Existence and attractivity of almost periodic solution for recurrent neural networks with unbounded delays and variable coefficients. Nonlinear Dyn., 2006, 45, 337–351.
12.
CaoJ.WangJ.Asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits Syst. I. Fundam. Theory Appl., 2003, 50(1), 34–44.
13.
CaoJ.SongQ.Stability in Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays. Nonlinearity, 2006, 19, 1601–1607.
14.
YuanK.CaoJ.Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays. Neurocomputing, 2006, 69, 1619–1627.
15.
ZhangQ.WeiX.XuJ.Stability analysis for cellular neural networks with variable delays. Chaos, Solitons Fractals, 2006, 28, 331–336.
16.
LiuB.HuangL.Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays. Phys. Let. A, 2006, 349, 177–186.
17.
SongQ.CaoJ.ZhaoZ.Periodic solutions and its exponential stability of reaction-diffusion recurrent neural networks with continuously distributed delays. Nonlinear Anal., Real World Appl., 2006, 7, 65–80.
18.
JiangH.TengZ.Global exponential stability of cellular neural networks with time-varying coefficients and delays. Neural Networks, 2004, 17(10), 1415–1425.
19.
JiangH.TengZ.A new criterion on the global exponential stability for cellular neural networks with multiple time-varying delays. Phys. Let. A, 2005, 338, 461–471.
20.
ZengZ.WangJ.LiaoX.Stability analysis of delayed cellular neural networks described using cloning templates. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 2004, 51(11), 2313–2324.
21.
TuF.LiaoX.Estimation of exponential convergence rate and exponential stability for neural networks with time-varying delay. Chaos, Solitons Fractals, 2005, 26, 1499–1505.
22.
LiangJ.CaoJ.Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays. Chaos, Solitons Fractals, 2004, 22, 773–785.
23.
FortiM.TesiA.New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 1995, 42, 354–366.
24.
KuangJ.Applied inequalities, Third edition (Shandong Science and Technology Press, Shandong Province, China).
