Paper Info
Title
A New Framework for Analysis on Stability and Bifurcation in a Class of Neural Networks With Discrete and Distributed Delays.
Abstract
This paper studies the stability and Hopf bifurcation in a class of high-dimension neural network involving the discrete and distributed delays under a new framework. By introducing some virtual neurons to the original system, the impact of distributed delay can be described in a simplified way via an equivalent new model. This paper extends the existing works on neural networks to high-dimension cases, which is much closer to complex and real neural networks. Here, we first analyze the Hopf bifurcation in this special class of high dimensional model with weak delay kernel from two aspects: one is induced by the time delay, the other is induced by a rate parameter, to reveal the roles of discrete and distributed delays on stability and bifurcation. Sufficient conditions for keeping the original system to be stable, and undergoing the Hopf bifurcation are obtained. Besides, this new framework can also apply to deal with the case of the strong delay kernel and corresponding analysis for different dynamical behaviors is provided. Finally, the simulation results are presented to justify the validity of our theoretical analysis.
Year
DOI
Venue
2015
10.1109/TCYB.2014.2367591
IEEE transactions on cybernetics
Keywords
Field
DocType
neural network,bifurcation,virtual node,stability,high dimensional,kernel,stability analysis
Kernel (linear algebra),Topology,Mathematical optimization,Biological applications of bifurcation theory,Control theory,Dimensional modeling,Artificial neural network,Hopf bifurcation,Mathematics,Bifurcation
Journal
Volume
Issue
ISSN
PP
99
2168-2275
Citations 
PageRank 
References 
42
1.12
19
Authors
5
Name
Order
Citations
PageRank
Wenying Xu11988.81
Jinde Cao211399733.03
Min Xiao3853.36
Daniel W.C. Ho45311285.38
Guanghui Wen52100113.74