Turing structures and turbulence in a chemical reaction-diffusion system

1995 ◽  
Vol 3 (2) ◽  
pp. 215-235 ◽  
Author(s):  
O. Jensen ◽  
V. O. Pannbacker ◽  
E. Mosekilde ◽  
G. Dewel ◽  
P. Borckmans
Keyword(s):  
Chemical Reaction ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Turing Structures

Superlattice Turing Structures in a Photosensitive Reaction-Diffusion System

2003 ◽  
Vol 91 (5) ◽  
Author(s):  
Igal Berenstein ◽  
Lingfa Yang ◽  
Milos Dolnik ◽  
Anatol M. Zhabotinsky ◽  
Irving R. Epstein
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Turing Structures

scholarly journals Programmable patterns in a DNA-based reaction–diffusion system

Soft Matter ◽  
2020 ◽  
Vol 16 (14) ◽  
pp. 3555-3563 ◽  
Author(s):  
Sifang Chen ◽  
Georg Seelig
Keyword(s):  
Chemical Reaction ◽  
In Silico ◽  
Reaction Diffusion ◽  
Chemical Reaction Networks ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Reaction Networks ◽  
System P

We report programmable reaction–diffusion patterns in DNA-based hydrogels, simulated and designed in silico using chemical reaction networks.

scholarly journals Singular Hopf-bifurcation in a chemical reaction-diffusion system

1998 ◽  
Vol 11 (4) ◽  
pp. 127-131
Author(s):  
M. Mimura ◽  
M. Nagayama ◽  
K. Sakamoto
Keyword(s):  
Hopf Bifurcation ◽  
Chemical Reaction ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System

Stationary Structures in a Discrete Bistable Reaction–Diffusion System

1997 ◽  
Vol 07 (12) ◽  
pp. 2807-2825 ◽  
Author(s):  
Alberto P. Muñuzuri ◽  
Leon O. Chua
Keyword(s):  
Three Dimensional ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Spatial Constraints ◽  
Intrinsic Nature ◽  
Turing Structures

A detailed description of the stationary patterns observed in one-, two- and three-dimensional bistable reaction–difusion media is presented. Because of the intrinsic nature of the system, no spatial constraints are found and completely new structures arise. The mechanism stabilizing these patterns is similar to the Turing structures case for a monostable media. The most important factors determining the final stationary structures observed are also stressed out.

Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster
Keyword(s):  
Reaction Diffusion ◽  
Dominant Mode ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Perturbation ◽  
Dimensional System ◽  
One Dimensional ◽  
Brusselator Model ◽  
The One ◽  
Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

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