Bifurcation Analysis and Spatiotemporal Patterns of Nonlinear Oscillations in a Ring Lattice of Identical Neurons with Delayed Coupling
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-29
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
We investigate the dynamics of a delayed neural network model consisting of n identical neurons.
We first analyze stability of the zero solution and then study the effect of time delay on the dynamics of the system.
We also investigate the steady state bifurcations and their stability.
The direction and stability of the Hopf bifurcation and the pitchfork bifurcation are analyzed by using the derived normal forms on center manifolds.
Then, the spatiotemporal patterns of bifurcating periodic solutions are investigated by using the symmetric bifurcation theory, Lie group theory and S 1 -equivariant degree theory.
Finally, two neural network models with four or seven neurons are used to verify our theoretical results.
American Psychological Association (APA)
Jiang, Jiao& Song, Yongli. 2014. Bifurcation Analysis and Spatiotemporal Patterns of Nonlinear Oscillations in a Ring Lattice of Identical Neurons with Delayed Coupling. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-18.
https://search.emarefa.net/detail/BIM-1013781
Modern Language Association (MLA)
Jiang, Jiao& Song, Yongli. Bifurcation Analysis and Spatiotemporal Patterns of Nonlinear Oscillations in a Ring Lattice of Identical Neurons with Delayed Coupling. Abstract and Applied Analysis No. 2014 (2014), pp.1-18.
https://search.emarefa.net/detail/BIM-1013781
American Medical Association (AMA)
Jiang, Jiao& Song, Yongli. Bifurcation Analysis and Spatiotemporal Patterns of Nonlinear Oscillations in a Ring Lattice of Identical Neurons with Delayed Coupling. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-18.
https://search.emarefa.net/detail/BIM-1013781
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013781