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Numerical Challenges for Resolving Spike Dynamics for Two One-Dimensional Reaction-Diffusion Systems.
- Source :
-
Studies in Applied Mathematics . Jul2003, Vol. 111 Issue 1, p41-84. 44p. - Publication Year :
- 2003
-
Abstract
- Asymptotic and numerical methods are used to highlight different types of dynamical behaviors that occur for the motion of a localized spike-type solution to the singularly perturbed Gierer–Meinhardt and Schnakenberg reaction-diffusion models in a one-dimensional spatial domain. Depending on the parameter range in these models, there can either be a slow evolution of a spike toward the midpoint of the domain, a sudden oscillatory instability triggered by a Hopf bifurcation leading to an intricate temporal oscillation in the height of the spike, or a pulse-splitting instability leading to the creation of new spikes in the domain. Criteria for the onset of these oscillatory and pulse-splitting instabilities are obtained through asymptotic and numerical techniques. A moving-mesh numerical method is introduced to compute these different behaviors numerically, and results are compared with corresponding results computed using a method of lines based software package. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SPATIAL analysis (Statistics)
*H-spaces
*COMPUTER software
*DYNAMICS
Subjects
Details
- Language :
- English
- ISSN :
- 00222526
- Volume :
- 111
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Studies in Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 9933252
- Full Text :
- https://doi.org/10.1111/1467-9590.t01-1-00227