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Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time Delay
Joint Authors
Gan, Qintao
Lv, Tianshi
Zhu, Qikai
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-01-19
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
Considering the fact that results for static neural networks are much more scare than results for local field neural networks and our purpose letting the problem researched be more general in many aspects, in this paper, a generalized neural networks model which includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks is built and the stability and bifurcation problems for it are investigated under Neumann boundary conditions.
First, by discussing the corresponding characteristic equations, the local stability of the trivial uniform steady state is discussed and the existence of Hopf bifurcations is shown.
By using the normal form theory and the center manifold reduction of partial function differential equations, explicit formulae which determine the direction and stability of bifurcating periodic solutions are acquired.
Finally, numerical simulations show the results.
American Psychological Association (APA)
Lv, Tianshi& Gan, Qintao& Zhu, Qikai. 2016. Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time Delay. Discrete Dynamics in Nature and Society،Vol. 2016, no. 2016, pp.1-9.
https://search.emarefa.net/detail/BIM-1103444
Modern Language Association (MLA)
Lv, Tianshi…[et al.]. Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time Delay. Discrete Dynamics in Nature and Society No. 2016 (2016), pp.1-9.
https://search.emarefa.net/detail/BIM-1103444
American Medical Association (AMA)
Lv, Tianshi& Gan, Qintao& Zhu, Qikai. Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time Delay. Discrete Dynamics in Nature and Society. 2016. Vol. 2016, no. 2016, pp.1-9.
https://search.emarefa.net/detail/BIM-1103444
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1103444