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Z 2 × Z 3 Equivariant Bifurcation in Coupled Two Neural Network Rings
Joint Authors
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-12-30
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
We study a Hopfield-type network that consists of a pair of one-way rings each with three neurons and two-way coupling between the rings.
The rings have symmetric group Γ=Z3×Z2, which means the global symmetry Z2 and internal symmetry Z3.
We discuss the spatiotemporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups.
The existence of multiple branches of bifurcating periodic solution is obtained.
We also found that the spatiotemporal patterns of bifurcating periodic oscillations alternate according to the change of the propagation time delay in the coupling; that is, different ranges of delays correspond to different patterns of neural network oscillators.
The oscillations of corresponding neurons in the two loops can be in phase, antiphase, T/3, 2T/3, 4T/3, 5T/6, or 7T/6 periods out of phase depending on the delay.
Some numerical simulations support our analysis results.
American Psychological Association (APA)
Zheng, Baodong& Yin, Haidong. 2014. Z 2 × Z 3 Equivariant Bifurcation in Coupled Two Neural Network Rings. Discrete Dynamics in Nature and Society،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1035043
Modern Language Association (MLA)
Zheng, Baodong& Yin, Haidong. Z 2 × Z 3 Equivariant Bifurcation in Coupled Two Neural Network Rings. Discrete Dynamics in Nature and Society No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-1035043
American Medical Association (AMA)
Zheng, Baodong& Yin, Haidong. Z 2 × Z 3 Equivariant Bifurcation in Coupled Two Neural Network Rings. Discrete Dynamics in Nature and Society. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1035043
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1035043