Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 14, Issue 2, Pages 1191-1202Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2012.09.010
Keywords
Codimension two bifurcation; Zero-Hopf bifurcation; Double Hopf bifurcation; Delayed neural networks
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Funding
- National Natural Science Foundation of China [60974020]
- Fundamental Research Funds for the Central Universities of China [CDJZR10 18 55 01]
- NPRP Grant, Qatar National Research Fund (a member of the Qatar Foundation) [4-1162-1-181]
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In this paper, a delayed neural network model with unidirectional coupling is considered. Zero-Hopf bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm form at the zero-Hopf singularity and show that the model can exhibit pitchfork, Hopf bifurcation, and double Hopf bifurcation is also found to occur in this model. Some numerical simulations are given to support the analytic results. (C) 2012 Elsevier Ltd. All rights reserved.
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