A new stability condition for discrete time recurrent neural networks with complex-valued linear threshold neurons

2014 ◽  
Author(s):  
Wei Zhou ◽  
Jacek M. Zurada
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Stability Condition ◽  
Recurrent Neural Networks ◽  
Linear Threshold ◽  
Linear Threshold Neurons ◽  
Complex Valued

Global Stability Analysis for Complex-Valued Recurrent Neural Networks and Its Application to Convex Optimization Problems

2009 ◽  
pp. 104-122 ◽  
Author(s):  
Mitsuo Yoshida ◽  
Takehiro Mori
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Global Stability ◽  
Discrete Time ◽  
Recurrent Neural Networks ◽  
Continuous Time ◽  
Stability Conditions ◽  
Global Stability Analysis ◽  
Solution Methods ◽  
Complex Valued

Global stability analysis for complex-valued artificial recurrent neural networks seems to be one of yet-unchallenged topics in information science. This chapter presents global stability conditions for discrete-time and continuous- time complex-valued recurrent neural networks, which are regarded as nonlinear dynamical systems. Global asymptotic stability conditions for these networks are derived by way of suitable choices of activation functions. According to these stability conditions, there are classes of discrete-time and continuous-time complex-valued recurrent neural networks whose equilibrium point is globally asymptotically stable. Furthermore, the conditions are shown to be successfully applicable to solving convex programming problems, for which real field solution methods are generally tedious.

Competitive Layer Model of Discrete-Time Recurrent Neural Networks with LT Neurons

2010 ◽  
Vol 22 (8) ◽  
pp. 2137-2160 ◽  
Author(s):  
Wei Zhou ◽  
Jacek M. Zurada
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Recurrent Neural Networks ◽  
Iteration Method ◽  
Storage Allocation ◽  
Layer Model ◽  
Linear Threshold ◽  
Iteration Methods ◽  
Winner Take All ◽  
And Storage

This letter discusses the competitive layer model (CLM) for a class of discrete-time recurrent neural networks with linear threshold (LT) neurons. It first addresses the boundedness, global attractivity, and complete stability of the networks. Two theorems are then presented for the networks to have CLM property. We also present the analysis for network dynamics, which performs a column winner-take-all behavior and grouping selection among different layers. Furthermore, we propose a novel synchronous CLM iteration method, which has similar performance and storage allocation but faster convergence compared with the previous asynchronous CLM iteration method (Wersing, Steil, & Ritter, 2001 ). Examples and simulation results are used to illustrate the developed theory, the comparison between two CLM iteration methods, and the application in image segmentation.

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