GLOBAL STABILITY ANALYSIS IN CELLULAR NEURAL NETWORKS WITH UNBOUNDED TIME DELAYS

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (6): 686-693.

GLOBAL STABILITY ANALYSIS IN CELLULAR NEURAL NETWORKS WITH UNBOUNDED TIME DELAYS

张继业

National Traction Power Laboratory, Southwest Jiaotong University, Chengdu 610031, P. R. China

收稿日期:2002-02-28 修回日期:2003-12-05 出版日期:2004-06-18 发布日期:2004-06-18
基金资助:
the National Natural Science Foundation of China(10272091)

GLOBAL STABILITY ANALYSIS IN CELLULAR NEURAL NETWORKS WITH UNBOUNDED TIME DELAYS

ZHANG Ji-ye

National Traction Power Laboratory, Southwest Jiaotong University, Chengdu 610031, P. R. China

Received:2002-02-28 Revised:2003-12-05 Online:2004-06-18 Published:2004-06-18
Supported by:
the National Natural Science Foundation of China(10272091)

摘要/Abstract

摘要： Without assuming the boundedness and differentiability of the activation functions, the conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of cellular neural networks with unbounded time delays and variable delays were studied. Using the idea of vector Liapunov method, the intero-differential inequalities with unbounded delay and variable delays were constructed. By the stability analysis of the intero-differential inequalities, the sufficient conditions for global asymptotic stability of cellular neural networks were obtained.

Abstract: Without assuming the boundedness and differentiability of the activation functions, the conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of cellular neural networks with unbounded time delays and variable delays were studied. Using the idea of vector Liapunov method, the intero-differential inequalities with unbounded delay and variable delays were constructed. By the stability analysis of the intero-differential inequalities, the sufficient conditions for global asymptotic stability of cellular neural networks were obtained.

中图分类号:

O317
TP711

张继业. GLOBAL STABILITY ANALYSIS IN CELLULAR NEURAL NETWORKS WITH UNBOUNDED TIME DELAYS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(6): 686-693.

ZHANG Ji-ye. GLOBAL STABILITY ANALYSIS IN CELLULAR NEURAL NETWORKS WITH UNBOUNDED TIME DELAYS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(6): 686-693.

参考文献

[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] Chua L O.CNN:A Paradigm for Complexity[M].Singapore:World Scientific,1998.
[4] Arik S,Tavanoglu V.Equilibrium analysis of delayed CNNs[J].IEEE Trans Circuits Syst Ⅰ,1998,45(2):168-171.
[5] Civalleri P P,Gill L M,Pandolfi L.On stability of cellular neural networks with delay[J].IEEE Trans Circuits Syst Ⅰ,1993,40(3):157-164.
[6] Roska T,Wu C W,Balsi M,et al.Stability and dynamics of delay-type general and cellular neural networks[J].IEEE Trans Circuits Syst,1992,39(6):487-490.
[7] Roska T,Wu C W,Balsi M,et al.Stability of cellular neural networks with dominant nonlinear and delay-type templates[J].IEEE Trans Circuits Syst,1993,40(4):270-272.
[8] Arik S,Tavanoglu V.On the global asymptotic stability of delayed cellular neural networks[J].IEEE Trans Circuits Syst Ⅰ,2000,47(4):571-574.
[9] ZHANG Ji-ye.Absolutely exponential stability in delayed cellular neural networks[J].Internat J Circuit Theory Appl,2002,30(4):395-409.
[10] Lu H.On stability of nonlinear continuous-time neural networks with delays[J].Neural Networks,2000,13(10):1135-1143.
[11] CAO Jin-de,LIN Yi-ping.Stability of a class of neural network models with delay [J].Applied Mathematics and Mechanics(English Edition),1999,20(8):912-916.
[12] Zhang Q,Ma R,Xu J.Stability of cellular neural networks with delay[J].Electronics Letters,2001,37(9):575-576.
[13] Gopalsamy K,He X.Stability in asymmetric Hopfield nets with transmission delays[J].Physica D,1994,76:344-358.
[14] Sree Hari Rao V,Phaneendra Bh R M.Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zones[J].Neural Networks,1999,12(3):455-465.
[15] ZHANG Ji-ye,JIN Xue-song.Global stability analysis in delayed Hopfield neural networks models[J].Neural Networks,2000,13(7):745-753.
[16] ZHANG Ji-ye,YANG Yi-ren.Global stability analysis of bidirectional associative memory neural networks with time delay[J].Internat J Circuit Theory Appl,2001,29(2):185-196.
[17] ZHANG Ji-ye.Global stability analysis in delayed cellular neural networks[J].Computers and Mathematics With Applications,2003,45(10/11):1707-1720.
[18] Zhang Y,Peng P A,Leung K S.Convergence analysis of cellular neural networks with unbounded delay[J].IEEE Trans Circuits Syst Ⅰ,2001,48(6):680-687.
[19] Forti M,Tesi A.New conditions for global stability of neural networks with application to linear and quadratic programming problems[J].IEEE Trans Circuits Syst Ⅰ,1995,42(7):354-366.
[20] SHU Zhong-zhou,ZHANG Ji-ye,CAO Deng-qing.Stability of Motion[M].Beijing:China Railway Publishing House,2001.(in Chinese)
[21] Siljiak D D.Large-Scale Dynamic Systems-Stability and Structure[M].New York:Elsevier North-Holland,Inc,1978.
[22] ZHANG Ji-ye,YANG Yi-ren,ZENG Jin.String stability of infinite interconnected system[J].Applied Mathematics and Mechanics(English Edition),2000,21(7):791-796.
[23] ZHANG Ji-ye.Globally exponential stability of neural networks with variable delays[J].IEEE Trans Circuits Syst Ⅰ,2003,50(2):288-291.
[24] Hale J.Theory of Functional Differential Equations[M].New York:Springer-Verlag,1977.

GLOBAL STABILITY ANALYSIS IN CELLULAR NEURAL NETWORKS WITH UNBOUNDED TIME DELAYS

GLOBAL STABILITY ANALYSIS IN CELLULAR NEURAL NETWORKS WITH UNBOUNDED TIME DELAYS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

编辑推荐

Metrics

本文评价

[1]	赵陆海波胡国辉周哲玮. Linear instability of ultra-thin liquid films flowing down cylindrical fibre[J]. Applied Mathematics and Mechanics (English Edition), 2011, 2(32): 133-140.
[2]	杨晓东;陈立群. DYNAMIC STABILITY OF AXIALLY MOVING VISCOELASTIC BEAMS WITH PULSATING SPEED[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(8): 989-995 .
[3]	齐朝晖;Alexander P.Seyranian. ON THE STABILITY BOUNDARY OF HAMILTONIAN SYSTEMS[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(2): 187-193.