Abstract
We classify generic instabilities of wave trains in reaction-diffusion systems on the real line as the wavenumber and system parameters are varied. We find three types of robust instabilities: Hopf with nonzero modulational wavenumber, sideband and spatio-temporal period-doubling. Near a fold, the only other robust instability mechanism, we show that all wave trains are necessarily unstable. We also discuss the special cases of homogeneous oscillations and reflection symmetric, stationary Turing patterns.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2679-2691 |
| Number of pages | 13 |
| Journal | International Journal of Bifurcation and Chaos |
| Volume | 17 |
| Issue number | 8 |
| DOIs | |
| State | Published - Aug 2007 |
Bibliographical note
Funding Information:This work was partially supported by the National Science Foundation through grant NSF DMS-0504271 (A. Scheel), and the Priority Program SPP 1095 of the DFG as well as the NDNS+ cluster of the NWO (J. Rademacher).
Keywords
- Classification of instabilities
- Reaction-diffusion systems
- Stability
- Wave trains