Some multistability properties of bidirectional associative memory recurrent neural networks with unsaturating piecewise linear transfer functions

2009 ◽  
Vol 72 (16-18) ◽  
pp. 3809-3817 ◽  
Author(s):  
Lei Zhang ◽  
Zhang Yi ◽  
Jiali Yu ◽  
Pheng Ann Heng
Keyword(s):  
Neural Networks ◽  
Associative Memory ◽  
Recurrent Neural Networks ◽  
Transfer Functions ◽  
Piecewise Linear ◽  
Bidirectional Associative Memory

Multistability Analysis for Recurrent Neural Networks with Unsaturating Piecewise Linear Transfer Functions

2003 ◽  
Vol 15 (3) ◽  
pp. 639-662 ◽  
Author(s):  
Zhang Yi ◽  
K. K. Tan ◽  
T. H. Lee
Keyword(s):  
Neural Networks ◽  
Decision Making ◽  
Recurrent Neural Networks ◽  
Complete Convergence ◽  
Global Attractivity ◽  
Transfer Functions ◽  
Piecewise Linear ◽  
Convergence Conditions ◽  
Local Inhibition ◽  
Attractive Sets

Multistability is a property necessary in neural networks in order to enable certain applications (e.g., decision making), where monostable networks can be computationally restrictive. This article focuses on the analysis of multistability for a class of recurrent neural networks with unsaturating piecewise linear transfer functions. It deals fully with the three basic properties of a multistable network: boundedness, global attractivity, and complete convergence. This article makes the following contributions: conditions based on local inhibition are derived that guarantee boundedness of some multistable networks, conditions are established for global attractivity, bounds on global attractive sets are obtained, complete convergence conditions for the network are developed using novel energy-like functions, and simulation examples are employed to illustrate the theory thus developed.

Robust stability analysis for delayed Cohen-Grossberg-type bidirectional associative memory neural networks with norm-bounded uncertainties

2009 ◽  
Vol 223 (5) ◽  
pp. 693-707
Author(s):  
Y Wang ◽  
P Hu
Keyword(s):  
Neural Networks ◽  
Associative Memory ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Bidirectional Associative Memory ◽  
Parameter Uncertainties ◽  
Robust Stability Analysis ◽  
Global Robust Stability ◽  
Bounded Uncertainties

In this paper, the problem of global robust stability is discussed for uncertain Cohen-Grossberg-type (CG-type) bidirectional associative memory (BAM) neural networks (NNs) with delays. The parameter uncertainties are supposed to be norm bounded. The sufficient conditions for global robust stability are derived by employing a Lyapunov-Krasovskii functional. Based on these, the conditions ensuring global asymptotic stability without parameter uncertainties are established. All conditions are expressed in terms of linear matrix inequalities (LMIs). In addition, two examples are provided to illustrate the effectiveness of the results obtained.

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