scholarly journals Effect of Spatial Average on the Spatiotemporal Pattern Formation of Reaction-Diffusion Systems

2021 ◽  
Author(s):  
Qingyan Shi ◽  
Junping Shi ◽  
Yongli Song
Keyword(s):  
Pattern Formation ◽  
Reaction Diffusion ◽  
Spatiotemporal Pattern ◽  
Spatial Average ◽  
Reaction Diffusion Systems ◽  
Spatiotemporal Pattern Formation ◽  
Diffusion Systems

A New Mechanical Algorithm for Calculating the Amplitude Equation of the Reaction-Diffusion Systems

2011 ◽  
pp. 205-213
Author(s):  
Houye Liu ◽  
Weiming Wang
Keyword(s):  
Hopf Bifurcation ◽  
Pattern Formation ◽  
Normal Form ◽  
Reaction Diffusion ◽  
Amplitude Equation ◽  
Diffusion Reaction ◽  
Future Studies ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Form Approach

Amplitude equation may be used to study pattern formatio. In this chapter, we establish a new mechanical algorithm AE_Hopf for calculating the amplitude equation near Hopf bifurcation based on the method of normal form approach in Maple. The normal form approach needs a large number of variables and intricate calculations. As a result, deriving the amplitude equation from diffusion-reaction is a difficult task. Making use of our mechanical algorithm, we derived the amplitude equations from several biology and physics models. The results indicate that the algorithm is easy to apply and effective. This algorithm may be useful for learning the dynamics of pattern formation of reaction-diffusion systems in future studies.

LEEM and MEM Studies of Spatiotemporal Pattern Formation

1998 ◽  
Vol 05 (06) ◽  
pp. 1233-1239 ◽  
Author(s):  
K. C. Rose ◽  
W. Engel ◽  
F. Meißen ◽  
A. J. Patchett ◽  
A. M. Bradshaw ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Pattern Formation ◽  
Reaction Diffusion ◽  
Low Energy ◽  
Spatiotemporal Pattern ◽  
Oxidation Of Co ◽  
Spatiotemporal Pattern Formation ◽  
Low Energy Electron ◽  
Stationary Conditions ◽  
Global Coupling

Spatiotemporal pattern formation has been investigated with low energy electron microscopy (LEEM) and mirror electron microscopy (MEM) during the catalytic oxidation of CO on Pt{110} under both oscillatory and stationary conditions. Due to higher resolution and richer contrast than in previous PEEM studies, it has been possible to investigate the details of the nucleation and propagation of reaction–diffusion fronts which make up the patterns, Further, new and more complex patterns have been discovered which demonstrate the importance of both global coupling and reaction-induced roughening.

Pattern formation in reaction diffusion systems: a Galerkin model

2001 ◽  
Vol 21 (4) ◽  
pp. 561-566 ◽  
Author(s):  
A. Bhattacharyay ◽  
J.K. Bhattacharjee
Keyword(s):  
Pattern Formation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems
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