Document Detail


Complex and chaotic dynamics in a discrete-time-delayed Hopfield neural network with ring architecture.
MedLine Citation:
PMID:  19386470     Owner:  NLM     Status:  MEDLINE    
Abstract/OtherAbstract:
This paper is devoted to the analysis of a discrete-time-delayed Hopfield-type neural network of p neurons with ring architecture. The stability domain of the null solution is found, the values of the characteristic parameter for which bifurcations occur at the origin are identified and the existence of Fold/Cusp, Neimark-Sacker and Flip bifurcations is proved. These bifurcations are analyzed by applying the center manifold theorem and the normal form theory. It is proved that resonant 1:3 and 1:4 bifurcations may also be present. It is shown that the dynamics in a neighborhood of the null solution become more and more complex as the characteristic parameter grows in magnitude and passes through the bifurcation values. A theoretical proof is given for the occurrence of Marotto's chaotic behavior, if the magnitudes of the interconnection coefficients are large enough and at least one of the activation functions has two simple real roots.
Authors:
Eva Kaslik; Stefan Balint
Publication Detail:
Type:  Journal Article     Date:  2009-03-26
Journal Detail:
Title:  Neural networks : the official journal of the International Neural Network Society     Volume:  22     ISSN:  1879-2782     ISO Abbreviation:  Neural Netw     Publication Date:  2009 Dec 
Date Detail:
Created Date:  2009-11-20     Completed Date:  2010-01-26     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  8805018     Medline TA:  Neural Netw     Country:  United States    
Other Details:
Languages:  eng     Pagination:  1411-8     Citation Subset:  IM    
Affiliation:
Department of Mathematics and Computer Science, West University of Timi??oara, Bd. V. P??rvan nr. 4, 300223, Timi??oara, Romania. kaslik@info.uvt.ro
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MeSH Terms
Descriptor/Qualifier:
Algorithms
Artificial Intelligence
Computer Systems*
Linear Models
Models, Neurological
Neural Networks (Computer)*
Neural Pathways / physiology
Neurons / physiology
Nonlinear Dynamics*

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine


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