EXISTENCE AND ATTRACTIVITY OF k-ALMOST AUTOMORPHIC SEQUENCE SOLUTION OF A MODEL OF CELLULAR NEURAL NETWORKS WITH DELAY

doi:10.1016/S0252-9602(12)60211-2

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (1): 290-302.doi: 10.1016/S0252-9602(12)60211-2

EXISTENCE AND ATTRACTIVITY OF k-ALMOST AUTOMORPHIC SEQUENCE SOLUTION OF A MODEL OF CELLULAR NEURAL NETWORKS WITH DELAY

Syed ABBAS|夏永辉*

School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, H.P. - 175001, India； Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

收稿日期:2011-03-05 修回日期:2011-11-08 出版日期:2013-01-20 发布日期:2013-01-20
通讯作者: 夏永辉，yhxia@zjnu.cn E-mail:sabbas.iitk@gmail.com; abbas@iitmandi.ac.in；yhxia@zjnu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (10901140, 11171090) and ZJNSFC (Y6100029, Y6100696, Y6110195).

EXISTENCE AND ATTRACTIVITY OF k-ALMOST AUTOMORPHIC SEQUENCE SOLUTION OF A MODEL OF CELLULAR NEURAL NETWORKS WITH DELAY

Syed ABBAS, XIA Yong-Hui*

School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, H.P. - 175001, India； Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Received:2011-03-05 Revised:2011-11-08 Online:2013-01-20 Published:2013-01-20
Contact: XIA Yong-Hui，yhxia@zjnu.cn E-mail:sabbas.iitk@gmail.com; abbas@iitmandi.ac.in；yhxia@zjnu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (10901140, 11171090) and ZJNSFC (Y6100029, Y6100696, Y6110195).

摘要/Abstract

摘要：

In this paper we discuss the existence and global attractivity of k-almost au-tomorphic sequence solution of a model of cellular neural networks. We consider the cor-responding difference equation analogue of the model system using suitable discretization method and obtain certain conditions for the existence of solution. Almost automorphic function is a good generalization of almost periodic function. This is the first paper con-sidering such solutions of the neural networks.

关键词: almost automorphic sequence, difference equations, neural networks

Abstract:

Key words: almost automorphic sequence, difference equations, neural networks

中图分类号:

34C27

Syed ABBAS, 夏永辉. EXISTENCE AND ATTRACTIVITY OF k-ALMOST AUTOMORPHIC SEQUENCE SOLUTION OF A MODEL OF CELLULAR NEURAL NETWORKS WITH DELAY[J]. 数学物理学报(英文版), 2013, 33(1): 290-302.

Syed ABBAS, XIA Yong-Hui. EXISTENCE AND ATTRACTIVITY OF k-ALMOST AUTOMORPHIC SEQUENCE SOLUTION OF A MODEL OF CELLULAR NEURAL NETWORKS WITH DELAY[J]. Acta mathematica scientia,Series B, 2013, 33(1): 290-302.

参考文献

[1] Abbas S. Pseudo almost periodic sequence solutions of discrete time cellular neural networks. Nonlinear Analysis, Modeling and Control, 2009, 14(3): 283–301

[2] Araya D, Castro R, Lizama C. Almost automorphic solutions of difference equations. Adv Differ Equ, 2009, 2009: pages 15

[3] Bohr H. Zur Theorie der fastperiodischen funktionen I. Acta Math, 1925, 45: 29–127

[4] Bochner S. Continuous mappings of almost automorphic and almost periodic functions. PNAS, 1964, 52: 907–910

[5] Cao J. New results concerning exponential stability and periodic solutions of delayed cellular neural net-works. Phys Lett A, 2003, 307(2/3): 136–147

[6] Cao J, Zhou D. Stability analysis of delayed cellular neural networks. Neural Networks, 1998, 11(9): 1601–1605

[7] Chen T. Global exponential stability of delayed hopfield neural networks. Neural Networks, 2001, 14(8): 977–980

[8] Hopfield J. Neurons with graded response have collective computational properties like those of two-state neurons. PNAS, 1984, 81: 3088–3092

[9] Hopfield J, Tank D. Computing with neural circuits. Model Science, 1986, 233: 3088–3092

[10] Huang Z K, Xia Y H, Wang X H. The existence and exponential attractivity of k-almost periodic sequence solution of discrete time neural networks. Nonlinear Dyn, 2007, 50: 13–26

[11] Huang Z K, Xia Y H, Wang X H. Exponential attractor of k-almost periodic sequence solution of discrete-time bidirectional neural networks. Sim Model Prac Theory, 2010, 18: 317–337

[12] Huang Z K, Xia Y H, Gao F. The existence and global attractivity of almost periodic sequence solution of discrete time neural networks. Phys Lett A, 2006, 350(3/4): 182–191

[13] Kosko B. Bidirectional associative memories. IEEE Trans Syst Man Cybern, 1988, 18(1): 49–60

[14] Kosko B. Adaptive bi-directional associative memories. Appl Opt, 1987, 26(23): 4947–4960

[15] Liao X X, Mao X. Exponential stability and instability of stochastic neural networks. Stoc Anal Appl, 1996, 14(2): 165–185

[16] Mohamad S, Gopalsamy K. Exponential stability of continuous-time and discrete-time cellular neural networks with delays. Appl Math Comp, 2003, 135(1): 17–38

[17] Yuan R. The existence of almost periodic solutions of retarded differential equations with piecewise constant argument. Nonlinear Anal, 2002, 48: 1013–1032

[18] Stewart I. Warning-handle with care. Nature, 1992, 355: 16–17

[19] Wiener J. A second-order delay differential equation with multiple periodic solutions. J Math Anal Appl, 1999, 229: 259–676

[20] Yang F J, Zhang C L, Chen C Y, Chen X M. Global exponential stability of a class of neural networks with delays. Acta Math Appli Sinica English Series, 2009, 25(1): 43–50

[21] Yang X, Wang Y, Huang L. Adaptive pinning synchronization of coupled neural networks with mixed delays and vector-form stochastic perturbations. Acta Mathematica Scientia, 2012, 32B(3): 955–977

[22] Fen Z, Cao J. Stability of a ring neural network with delays. Acta Mathematica Scientia, 2010, 30A(6): 1654–1665

EXISTENCE AND ATTRACTIVITY OF k-ALMOST AUTOMORPHIC SEQUENCE SOLUTION OF A MODEL OF CELLULAR NEURAL NETWORKS WITH DELAY

EXISTENCE AND ATTRACTIVITY OF k-ALMOST AUTOMORPHIC SEQUENCE SOLUTION OF A MODEL OF CELLULAR NEURAL NETWORKS WITH DELAY

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