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| Content Provider | Springer Nature Link |
|---|---|
| Author | Guo, Shang Jiang Chen, Yu Ming Wu, Jian Hong |
| Copyright Year | 2011 |
| Abstract | In this paper, we develop an efficient approach to compute the equivariant normal form of delay differential equations with parameters in the presence of symmetry. We present and justify a process that involves center manifold reduction and normalization preserving the symmetry, and that yields normal forms explicitly in terms of the coefficients of the original system. We observe that the form of the reduced vector field relies only on the information of the linearized system at the critical point and on the inherent symmetry, and the normal forms give critical information about not only the existence but also the stability and direction of bifurcated spatiotemporal patterns. We illustrate our general results by some applications to fold bifurcation, equivariant Hopf bifurcation and Hopf-Hopf interaction, with a detailed case study of additive neurons with delayed feedback. |
| Ending Page | 856 |
| Page Count | 32 |
| Starting Page | 825 |
| File Format | |
| ISSN | 14398516 |
| e-ISSN | 14397617 |
| Journal | Acta Mathematica Sinica, English Series |
| Issue Number | 4 |
| Volume Number | 28 |
| Language | English |
| Publisher | Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |
| Publisher Date | 2011-11-05 |
| Publisher Place | Heidelberg |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | bifurcation Symmetries, equivariant bifurcation theory Equivariant delay differential equation Bifurcation theory Mathematics equilibrium normal form stability Neural networks, artificial life and related topics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
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