scholarly journals A novel time efficient structure-preserving splitting method for the solution of two-dimensional reaction-diffusion systems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Nauman Ahmed ◽  
Alper Korkmaz ◽  
M. Rafiq ◽  
Dumitru Baleanu ◽  
Ali Saleh Alshomrani ◽  
...  
Keyword(s):  
Splitting Method ◽  
Reaction Diffusion ◽  
Two Dimensional ◽  
Structure Preserving ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems

Modulated two-dimensional patterns in reaction–diffusion systems

1999 ◽  
Vol 10 (2) ◽  
pp. 157-184 ◽  
Author(s):  
R. KUSKE ◽  
P. MILEWSKI
Keyword(s):  
Reaction Diffusion ◽  
Hexagonal Structure ◽  
Two Dimensional ◽  
Computational Approaches ◽  
Modulation Equations ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
New Phenomena ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

New modulation equations for hexagonal patterns in reaction–diffusion systems are derived for parameter régimes corresponding to the onset of patterns. These systems include additional nonlinearities which are not present in Rayleigh–Bénard convection or Swift–Hohenberg type models. The dynamics of hexagonal and roll patterns are studied using a combination of analytical and computational approaches which exploit the hexagonal structure of the modulation equations. The investigation demonstrates instabilities and new phenomena not found in other systems, and is applied to patterns of flame fronts in a certain model of burner stabilized flames.

PATTERN FORMATION IN CHEMOTAXIC REACTION-DIFFUSION SYSTEMS

2012 ◽  
Vol 05 (03) ◽  
pp. 1260013
Author(s):  
HIROTO SHOJI ◽  
KEITARO SAITOH
Keyword(s):  
Free Energy ◽  
Pattern Formation ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Volume Filling ◽  
Reaction Diffusion Systems ◽  
Receptor Aggregation ◽  
Diffusion Systems

In this study, we investigate two-dimensional patterns generated by chemotaxis reaction-diffusion systems. We numerically examine the Keller–Segel models with the volume-filling aggregation term and the receptor aggregation term in two dimensions. Spotted, striped and reversed spotted patterns are obtained as stable motionless equilibrium patterns. The relative stability of these patterns is studied numerically on the basis of the derived free energy. The intuitive understanding of these generated patterns and the relation with three-dimensional patterns are also discussed.

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