The Saddle-Node of Nearly Homogeneous Wave Trains in Reaction–Diffusion Systems

2006 ◽  
Vol 19 (2) ◽  
pp. 479-496 ◽  
Author(s):  
Jens D. M. Rademacher ◽  
Arnd Scheel
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Saddle Node ◽  
Diffusion Systems ◽  
Homogeneous Wave ◽  
Wave Trains

INSTABILITIES OF WAVE TRAINS AND TURING PATTERNS IN LARGE DOMAINS

2007 ◽  
Vol 17 (08) ◽  
pp. 2679-2691 ◽  
Author(s):  
JENS D. M. RADEMACHER ◽  
ARND SCHEEL
Keyword(s):  
Period Doubling ◽  
Reaction Diffusion ◽  
Turing Patterns ◽  
Instability Mechanism ◽  
Reaction Diffusion Systems ◽  
System Parameters ◽  
Diffusion Systems ◽  
Special Cases ◽  
Wave Trains ◽  
Spatio Temporal

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.

scholarly journals Diffusive mixing of periodic wave trains in reaction–diffusion systems

2012 ◽  
Vol 252 (5) ◽  
pp. 3541-3574 ◽  
Author(s):  
Björn Sandstede ◽  
Arnd Scheel ◽  
Guido Schneider ◽  
Hannes Uecker
Keyword(s):  
Reaction Diffusion ◽  
Periodic Wave ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Wave Trains ◽  
Diffusive Mixing
Sign in / Sign up

Export Citation Format

Share Document