Hopf Bifurcation Analysis for a Four-Dimensional Recurrent Neural Network with Two Delays
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-21
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
A four-dimensional recurrent neural network with two delays is considered.
The main result is given in terms of local stability and Hopf bifurcation.
Sufficient conditions for local stability of the zero equilibrium and existence of the Hopf bifurcation with respect to both delays are obtained by analyzing the distribution of the roots of the associated characteristic equation.
In particular, explicit formulae for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established by using the normal form theory and center manifold theory.
Some numerical examples are also presented to verify the theoretical analysis.
American Psychological Association (APA)
Zhang, Zizhen& Yang, Huizhong. 2013. Hopf Bifurcation Analysis for a Four-Dimensional Recurrent Neural Network with Two Delays. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-472121
Modern Language Association (MLA)
Zhang, Zizhen& Yang, Huizhong. Hopf Bifurcation Analysis for a Four-Dimensional Recurrent Neural Network with Two Delays. Journal of Applied Mathematics No. 2013 (2013), pp.1-13.
https://search.emarefa.net/detail/BIM-472121
American Medical Association (AMA)
Zhang, Zizhen& Yang, Huizhong. Hopf Bifurcation Analysis for a Four-Dimensional Recurrent Neural Network with Two Delays. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-472121
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-472121