Abstract
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. © 2012 Elsevier Ltd. All rights reserved.
| Original language | English |
|---|---|
| Pages (from-to) | 1191-1202 |
| Journal | Nonlinear Analysis: Real World Applications |
| Volume | 14 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Apr 2013 |
| Externally published | Yes |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Funding
The work is supported by the National Natural Science Foundation of China Grant No. 60974020 and the Fundamental Research Funds for the Central Universities of China (Project No. CDJZR10 18 55 01 ); the work is also supported by NPRP Grant 4-1162-1-181 from the Qatar National Research Fund (a member of the Qatar Foundation).
Research Keywords
- Codimension two bifurcation
- Delayed neural networks
- Double Hopf bifurcation
- Zero-Hopf bifurcation
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