Positive invariant and global exponential attractive sets of neural networks with time-varying delays

被引：69

作者：

Liao, Xiaoxin ^{[2
]}

Luo, Qi ^{[1
]}

Zeng, Zhigang ^{[1
]}

机构：

[1] Nanjing Univ Informat Sci & Technol, Dept Informat & Commun, Jiangsu 210044, Peoples R China

[2] Huazhong Univ Sci & Technol, Dept Control Sci & Engn, Wuhan 430074, Peoples R China

来源：

NEUROCOMPUTING | 2008年 / 71卷 / 4-6期

基金：

中国国家自然科学基金;

关键词：

positive invariant set; globally exponentially attractive set; Lagrange stability; neural networks;

D O I：

10.1016/j.neucom.2007.07.017

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

In this paper, global exponential stability in Lagrange sense is further studied for various continuous-time delayed recurrent neural network with two different types of activation functions. Based on the parameters of the systems, detailed estimation of global exponential attractive sets and positive invariant sets are presented without any hypothesis on the existence. It is also verified that outside the global exponential attracting set; i.e., within the global attraction domain, there is no equilibrium state, periodic state, almost periodic state, and chaos attractor of the neural network. These theoretical analysis narrows the search field of optimization computation, associative memories, chaos control and synchronization and provide convenience for applications. (c) 2007 Elsevier B.V. All rights reserved.

引用

页码：513 / 518

页数：6

共 19 条

[1]

CHUA LO, 1988, IEEE T CIRCUITS SYST, V35, P1272

[2] NECESSARY AND SUFFICIENT CONDITION FOR ABSOLUTE STABILITY OF NEURAL NETWORKS [J].

FORTI, M ;

MANETTI, S ;

MARINI, M .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 1994, 41 (07) :491-494

[3] NEURONS WITH GRADED RESPONSE HAVE COLLECTIVE COMPUTATIONAL PROPERTIES LIKE THOSE OF 2-STATE NEURONS [J].

HOPFIELD, JJ .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA-BIOLOGICAL SCIENCES, 1984, 81 (10) :3088-3092

[4]

Liao X., 2005, ADV SYST SCI APPL, V5, P533

[5] Robust stability for interval Hopfield neural networks with time delay [J].

Liao, XF ;

Yu, JB .

IEEE TRANSACTIONS ON NEURAL NETWORKS, 1998, 9 (05) :1042-1045

[6]

Liao XX, 2006, LECT NOTES COMPUT SC, V3971, P115

[7] Global dissipativity of continuous-time recurrent neural networks with time delay [J].

Liao, XX ;

Wang, J .

PHYSICAL REVIEW E, 2003, 68 (01) :7

[8] Algebraic criteria for global exponential stability of cellular neural networks with multiple time delays [J].

Liao, XX ;

Wang, J .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 2003, 50 (02) :268-275

[9]

LIAO XX, 1995, SCI CHINA SER A, V38, P407

[10]

LIAO XX, 1994, SCI CHINA SER A, V24, P902

← 1 2 →