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Target patterns and spiral waves in reaction-diffusion systems with limit cycle kinetics and weak diffusion

Target patterns and spiral waves in reaction-diffusion systems with limit cycle kinetics and weak... In this paper, we study periodic waves in reaction-diffusion systems with limit cycle kinetics and weak diffusion. The results are based on the analysis of nonlinear partial differential equation which is derived from singular perturbation techniques. We obtain the first order approximation expression of the dispersion curve for periodic wave trains and then show that in the generic case of limit cycle kinetics there is a one parameter family of target patterns and the rotating spiral waves of Archimedian type exist., Finally, we apply these results to the general λ−ω systems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Target patterns and spiral waves in reaction-diffusion systems with limit cycle kinetics and weak diffusion

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Publisher
Springer Journals
Copyright
Copyright © 1998 by Science Press
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02683817
Publisher site
See Article on Publisher Site

Abstract

In this paper, we study periodic waves in reaction-diffusion systems with limit cycle kinetics and weak diffusion. The results are based on the analysis of nonlinear partial differential equation which is derived from singular perturbation techniques. We obtain the first order approximation expression of the dispersion curve for periodic wave trains and then show that in the generic case of limit cycle kinetics there is a one parameter family of target patterns and the rotating spiral waves of Archimedian type exist., Finally, we apply these results to the general λ−ω systems.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 4, 2007

References