Multistability analysis of a general class of recurrent neural networks with non-monotonic activation functions and time-varying delays

2016 ◽  
Vol 79 ◽  
pp. 117-127 ◽  
Author(s):  
Peng Liu ◽  
Zhigang Zeng ◽  
Jun Wang
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
General Class ◽  
Time Varying ◽  
Activation Functions

Analysis and Design of Associative Memories Based on Recurrent Neural Networks with Linear Saturation Activation Functions and Time-Varying Delays

2007 ◽  
Vol 19 (8) ◽  
pp. 2149-2182 ◽  
Author(s):  
Zhigang Zeng ◽  
Jun Wang
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Activation Functions ◽  
Analysis And Design ◽  
Design Procedures ◽  
The Neural Network ◽  
Saturation Region ◽  
The Neural Networks

In this letter, some sufficient conditions are obtained to guarantee recurrent neural networks with linear saturation activation functions, and time-varying delays have multiequilibria located in the saturation region and the boundaries of the saturation region. These results on pattern characterization are used to analyze and design autoassociative memories, which are directly based on the parameters of the neural networks. Moreover, a formula for the numbers of spurious equilibria is also derived. Four design procedures for recurrent neural networks with linear saturation activation functions and time-varying delays are developed based on stability results. Two of these procedures allow the neural network to be capable of learning and forgetting. Finally, simulation results demonstrate the validity and characteristics of the proposed approach.

scholarly journals Delay-Dependent Stability Analysis for Recurrent Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Shu Lv ◽  
Junkang Tian ◽  
Shouming Zhong
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Activation Functions ◽  
New Class ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper concerns the problem of delay-dependent stability criteria for recurrent neural networks with time varying delays. By taking more information of states and activation functions as augmented vectors, a new class of the Lyapunov functional is proposed. Then, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

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