Abstract
This brief reports a retarded functional differential equation modeling tri-neuron network with time delay. The Bogdanov-Takens (B-T) bifurcation is investigated by using the center manifold reduction and the normal form method. We get the versal unfolding of the norm forms at the B-T singularity and show that the model can exhibit pitchfork, Hopf, homoclinic, and double-limit cycles bifurcations. Some numerical simulations are given to support the analytic results and explore chaotic dynamics. Finally, an algorithm is given to show that chaotic tri-neuron networks can be used for encrypting a color image. © 2012 IEEE.
| Original language | English |
|---|---|
| Article number | 6478832 |
| Pages (from-to) | 1001-1007 |
| Journal | IEEE Transactions on Neural Networks and Learning Systems |
| Volume | 24 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 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 <a href="mailto:[email protected]">[email protected]</a>.Funding
This work was supported in part by the National Natural Science Foundation of China, under Grant 60974020, the Fundamental Research Funds for the Central Universities of China, under Project CDJZR10 18 55 01, and the National Priority Research Project, under Grant NPRP 4-1162-1-181 funded by Qatar National Research Fund, Qatar.
Research Keywords
- Bogdanov-Takens bifurcation
- homoclinic bifurcation
- tri-neuron network
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