Inwardly Rotating Spiral Waves in a Reaction-Diffusion System

Science ◽  
2001 ◽  
Vol 294 (5543) ◽  
pp. 835-837 ◽  
Author(s):  
V. K. Vanag
Keyword(s):  
Reaction Diffusion ◽  
Spiral Waves ◽  
Reaction Diffusion System ◽  
Diffusion System

Inducing and modulating spiral waves by delayed feedback in a uniform oscillatory reaction–diffusion system

2010 ◽  
Vol 371 (1-3) ◽  
pp. 60-65 ◽  
Author(s):  
Haixiang Hu ◽  
Xiaochun Li ◽  
Zhiming Fang ◽  
Xu Fu ◽  
Lin Ji ◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Delayed Feedback ◽  
Spiral Waves ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Oscillatory Reaction

SPIRAL WAVE MAINTAINED BY NOISE

2004 ◽  
Vol 04 (03) ◽  
pp. L447-452 ◽  
Author(s):  
AI ZHONG LEI ◽  
QIAN SHU LI ◽  
WEIGUO XU ◽  
DAIPING HU
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Noise Level ◽  
Gaussian White Noise ◽  
Spiral Wave ◽  
Reaction Diffusion ◽  
Spiral Waves ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Zero Level

The effect of Gaussian white noise on a chemical wavefront is studied in a modified FitzHugn–Nagumo model by applying numerical simulations. A rotating spiral waves can be formed if the medium is excitable enough and the fronts has a free end, when the reaction diffusion system is disturbed by a certain non-zero level noise. It is counterintuitive that noise plays a constructive role in the product and propagation of single spiral waves in this letter. Weak or strong noise will make against the product and propagation of spiral waves. In a certain noise level, spiral wave can be maintained in a medium, where such spiral waves cannot be observed in the absence of the noise.

Breathing spiral waves in the chlorine dioxide–iodine–malonic acid reaction-diffusion system

2008 ◽  
Vol 78 (2) ◽  
Author(s):  
Igal Berenstein ◽  
Alberto P. Muñuzuri ◽  
Lingfa Yang ◽  
Milos Dolnik ◽  
Anatol M. Zhabotinsky ◽  
...  
Keyword(s):  
Malonic Acid ◽  
Chlorine Dioxide ◽  
Reaction Diffusion ◽  
Spiral Waves ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Acid Reaction

scholarly journals Theory of spike spiral waves in a reaction-diffusion system

1999 ◽  
Vol 60 (1) ◽  
pp. 242-246 ◽  
Author(s):  
C. B. Muratov ◽  
V. V. Osipov
Keyword(s):  
Reaction Diffusion ◽  
Spiral Waves ◽  
Reaction Diffusion System ◽  
Diffusion System

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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