scholarly journals Existence of n-cycles and border-collision bifurcations in piecewise-linear continuous maps with applications to recurrent neural networks

2020 ◽  
Vol 101 (2) ◽  
pp. 1037-1052
Author(s):  
Z. Monfared ◽  
D. Durstewitz
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Piecewise Linear ◽  
Border Collision Bifurcations ◽  
Continuous Maps

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.

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.

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