[1] Liang Jinling,. Global exponential periodicityof a class of impulsive neural networks [J]. Journal of Southeast University (English Edition), 2005, 21 (4): 509-512. [doi:10.3969/j.issn.1003-7985.2005.04.027]

Copy

Global exponential periodicityof a class of impulsive neural networks()

Share：

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

21

Issue:

2005 4

Page:

509-512

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2005-12-30

Info

Title:

Global exponential periodicityof a class of impulsive neural networks

Author(s):

Liang Jinling

Department of Mathematics, Southeast University, Nanjing 210096, China

Keywords:

global exponential periodicity;  impulsive neural networks;  Lyapunov function;  Lipschitz activation function

PACS:

O175.12

DOI:

10.3969/j.issn.1003-7985.2005.04.027

Abstract:

By the Lyapunov function method, combined with the inequality techniques, some criteria are established to ensure the existence, uniqueness and global exponential stability of the periodic solution for a class of impulsive neural networks.The results obtained only require the activation functions to be globally Lipschitz continuous without assuming their boundedness, monotonicity or differentiability.The conditions are easy to check in practice and they can be applied to design globally exponentially periodic impulsive neural networks.

References:

[1] Chua L O, Yang L.Cellular neural networks:theory[J].IEEE Trans Circuits Syst, 1988, 35(10):1257-1272.
[2] Chua L O, Yang L.Cellular neural networks:applications[J].IEEE Trans Circuits Syst, 1988, 35(10):1273-1290.
[3] Cao J, Wang J.Global asymptotic stability of a general class of recurrent neural networks with time-varying delays[J].IEEE Trans Circuits Syst-I, 2003, 50(1):34-44.
[4] Arik S.An improved global stability result for delayed cellular neural networks[J].IEEE Trans Circuits Syst-I, 2002, 49(8):1211-1214.
[5] Liao X F, Wong K W, Wu Z.Asymptotic stability criteria for a two-layer network with different time delays[J].IEEE Trans Neural Networks, 2003, 14(1):222-227.
[6] Liang J, Cao J.Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delay[J]. Chaos, Solitons & Fractals, 2004, 22(4):773-785.
[7] Chen A, Cao J, Huang L.An estimation of upper bound of delays for global asymptotic stability of delayed Hopfield neural networks[J]. IEEE Trans Circuits Syst-I, 2002, 49(7):1028-1032.
[8] Guan Z H, Lam J, Chen G R.On impulsive auto-associative neural networks[J]. Neural Networks, 2000, 13(1):63-69.
[9] Bainov D D, Simeonov P S.Systems with impulse effect: stability theory and applications[M]. Chichester: Ellis Horwood, 1989.
[10] Sun J.Impulsive control of a new chaotic system[J].Math Comput Simulation, 2004, 64:669-677.
[11] Xie W, Wen C, Li Z.Impulsive control for the stabilization and synchronization of Lorenz systems[J].Phys Lett A, 2000, 275:67-72.
[12] Gopalsamy K.Stability of artificial neural networks with impulses[J].Appl Math Comput, 2004, 154(3):783-813.
[13] Chen B S, Wang J.Global exponential periodicity and global exponential stability of a class of recurrent neural networks[J]. Phys Lett A, 2004, 329:36-48.
[14] Xu S Y, Lam J, Ho W C, et al.Global robust exponential stability analysis for interval recurrent neural networks[J].Phys Lett A, 2004, 325:124-133.

Memo

Memo:

Biography: Liang Jinling(1974—), female, lecturer, jinlliang@seu.edu.cn.

Common functions