Stationary Periodical Structure Emitting an Infinite Number of Traveling Impulses in a Model of a One-Dimensional Infinite Excitable Reaction−Diffusion System

2009 ◽  
Vol 113 (13) ◽  
pp. 3133-3136 ◽  
Author(s):  
Andrzej L. Kawczyński
Keyword(s):  
Infinite Number ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
One Dimensional ◽  
Periodical Structure

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.

Nucleation Rate of a Localized Structure in a Reaction-Diffusion System

1993 ◽  
Vol 48 (5-6) ◽  
pp. 636-638 ◽  
Author(s):  
T. Christen
Keyword(s):  
Diffusion Equation ◽  
Nucleation Rate ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Reaction Diffusion Equation ◽  
One Dimensional ◽  
Uniform State

Abstract We derive the nucleation rate of a localized structure of a one-dimensional, nonlocal, bistable reaction diffusion equation near instability of the uniform state.

scholarly journals Traveling wave solutions for a class of reaction-diffusion system

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bingyi Wang ◽  
Yang Zhang
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Traveling Wave Solution ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
One Dimensional ◽  
Wave Solutions

AbstractIn this paper we investigate the existence of traveling wave for a one-dimensional reaction diffusion system. We show that this system has a unique translation traveling wave solution.

scholarly journals Numerical Approximation to Nonlinear One Dimensional Coupled Reaction Diffusion System

2017 ◽  
Vol 05 (08) ◽  
pp. 1551-1574 ◽  
Author(s):  
Shahid Hasnain ◽  
Daoud Suleiman Mashat ◽  
Muhammad Saqib ◽  
Shafeek A. Ghaleb ◽  
Noorah Y. Mshary
Keyword(s):  
Numerical Approximation ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
One Dimensional ◽  
Coupled Reaction
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