Spatio-temporal dynamics of a reaction–diffusion equation with the nonlocal spatial average and delay

2020 ◽  
Vol 107 ◽  
pp. 106388
Author(s):  
Yongli Song ◽  
Gaoxiang Yang
Keyword(s):  
Diffusion Equation ◽  
Temporal Dynamics ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Spatial Average ◽  
Spatio Temporal

Spatio-temporal pattern formation in a nonlocal reaction-diffusion equation

2001 ◽  
Vol 16 (2) ◽  
pp. 173-192 ◽  
Author(s):  
S. A. Gourley ◽  
M. A. J. Chaplain ◽  
F. A. Davidson
Keyword(s):  
Pattern Formation ◽  
Diffusion Equation ◽  
Temporal Pattern ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Spatio Temporal ◽  
Nonlocal Reaction

scholarly journals Amplitude Equations and Chemical Reaction–Diffusion Systems

1997 ◽  
Vol 07 (07) ◽  
pp. 1539-1554 ◽  
Author(s):  
M. Ipsen ◽  
F. Hynne ◽  
P. G. Sørensen
Keyword(s):  
Diffusion Equation ◽  
Chemical Reaction ◽  
Bifurcation Point ◽  
Landau Equation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Amplitude Equations ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Spatio Temporal

The paper discusses the use of amplitude equations to describe the spatio-temporal dynamics of a chemical reaction–diffusion system based on an Oregonator model of the Belousov–Zhabotinsky reaction. Sufficiently close to a supercritical Hopf bifurcation the reaction–diffusion equation can be approximated by a complex Ginzburg–Landau equation with parameters determined by the original equation at the point of operation considered. We illustrate the validity of this reduction by comparing numerical spiral wave solutions to the Oregonator reaction–diffusion equation with the corresponding solutions to the complex Ginzburg–Landau equation at finite distances from the bifurcation point. We also compare the solutions at a bifurcation point where the systems develop spatio-temporal chaos. We show that the complex Ginzburg–Landau equation represents the dynamical behavior of the reaction–diffusion equation remarkably well, sufficiently far from the bifurcation point for experimental applications to be feasible.

Spatio-temporal pattern formation in a nonlocal reaction-diffusion equation

2001 ◽  
Vol 16 (2) ◽  
pp. 173-192 ◽  
Author(s):  
S. A. Gourley ◽  
M. A. J. Chaplain ◽  
F. A. Davidson
Keyword(s):  
Pattern Formation ◽  
Diffusion Equation ◽  
Temporal Pattern ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Spatio Temporal ◽  
Nonlocal Reaction
Sign in / Sign up

Export Citation Format

Share Document