Multistability of Discrete-Time Recurrent Neural Networks With Unsaturating Piecewise Linear Activation Functions

2004 ◽  
Vol 15 (2) ◽  
pp. 329-336 ◽  
Author(s):  
Z. Yi ◽  
K.K. Tan
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Recurrent Neural Networks ◽  
Piecewise Linear ◽  
Activation Functions

Globally Exponentially Stability of Discrete-Time Recurrent Neural Networks with Unsaturating Linear Activation Functions

2011 ◽  
Vol 467-469 ◽  
pp. 731-736
Author(s):  
Zong Bing Lin ◽  
Qian Rong Tan ◽  
Jun Li
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Recurrent Neural Networks ◽  
Matrix Theory ◽  
Activation Functions ◽  
Energy Functions ◽  
Matrix Eigenvalue ◽  
Definition Of

Globally exponentially stability (GES) of a class of discrete- time recurrent neural networks with unsaturating linear activation functions is studied. Based on matrix eigenvalue, a new definition of GES is presented. By applying matrix theory, some conditions for GES are obtained. Simultaneously, those conditions are proved without energy functions.

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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