Local stability analysis of high-order recurrent neural networks with multi-step piecewise linear activation functions

2013 ◽  
Author(s):  
Yujiao Huang ◽  
Huaguang Zhang ◽  
Dongsheng Yang
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Recurrent Neural Networks ◽  
Local Stability ◽  
Piecewise Linear ◽  
High Order ◽  
Activation Functions ◽  
Local Stability Analysis

Dynamical stability analysis of delayed recurrent neural networks with ring structure

2014 ◽  
Vol 28 (19) ◽  
pp. 1450118 ◽  
Author(s):  
Huaguang Zhang ◽  
Yujiao Huang ◽  
Tiaoyang Cai ◽  
Zhanshan Wang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Multiple Equilibria ◽  
Piecewise Linear ◽  
Ring Structure ◽  
Activation Functions ◽  
Model Stability ◽  
The Neural Network ◽  
Stability Results

In this paper, multistability is discussed for delayed recurrent neural networks with ring structure and multi-step piecewise linear activation functions. Sufficient criteria are obtained to check the existence of multiple equilibria. A lemma is proposed to explore the number and the cross-direction of purely imaginary roots for the characteristic equation, which corresponds to the neural network model. Stability of all of equilibria is investigated. The work improves and extends the existing stability results in the literature. Finally, two examples are given to illustrate the effectiveness of the obtained results.

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