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stability index analysis of 1-D patterns of the Gray-Scott model by A. Doelman

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Published by American Mathematical Society in Providence, R.I .
Written in English


  • Reaction-diffusion equations.,
  • Perturbation (Mathematics),
  • Eigenvalues.

Book details:

Edition Notes

StatementArjen Doelman, Robert A. Gardner, Tasso J. Kaper.
SeriesMemoirs of the American Mathematical Society -- no. 737.
ContributionsGardner, Robert A., 1950-, Kaper, Tasso J., 1964-
LC ClassificationsQA3 .A57 no. 737, QA377 .A57 no. 737
The Physical Object
Paginationxi, 64 p. ;
Number of Pages64
ID Numbers
Open LibraryOL17718564M
ISBN 100821827391
LC Control Number2001045832

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Get this from a library! A stability index analysis of 1-D patterns of the Gray-Scott model. [Arjen Doelman; Robert A Gardner; Tasso J Kaper]. Index Analysis will be useful for mathematicians working in category theory, topology, probability and statistics, functional analysis, and theoretical computer science. A Stability Index Analysis of 1-D Patterns of the Gray-Scott Model. ELSEVIER Physica D () PHYmA Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach Arjen Doelman a, Robert A. Gardner b, Tasso J. Kaper c,, a Mathematisch Instituut, Universiteit Utrecht, P.O. Box , TA Utrecht, Netherlands b Department of Mathematics, University of Massachusetts, Amherst, MA , USA c Department of Cited by: The next section presents the analysis of the Gray–Scott model. We finish with some discussion of numerical results and compare our numerical results with the results given in the Pearson paper. Our results are summarized in the following: Theorem. There exists nonuniform smooth steady solutions to the Gray–Scott system with d 1,d 2 >d>0, F Cited by:

Data modeler's workbench: tools and techniques for analysis and design / Steve Hoberman. PUBLISHER: New York ; Chichester [England]: Wiley, c CALL NUMBER: QA D26 H62 CIMM: AUTHOR: Dominich, Sándor. TITLE: Mathematical foundations of information retrieval / by Sándor Dominich. PUBLISHER. Abstract. We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction-diffusion systems with\ud fractional reaction rates such as the Sel'kov model, the\ud Gray-Scott system, the hypercycle Eigen and Schuster, angiogenesis, and the generalized Gierer-Meinhardt\ud system.\ud We give some sufficient and explicit conditions for stability\ud by Author: M Winter and J Wei. The existence and stability of localized patterns of criminal activity are studied for the reaction-diffusion model of urban crime that was introduced by Short et. al. [Math. Models. Meth. Appl. Sci., 18, Suppl. (), pp. ]. Such patterns, characterized by the concentration of criminal activity in localized spatial regions, are referred to as hot-spot patterns and they occur in a Cited by: Doelman, A., Gardner, R.A., Kaper, T.J.: Stability analysis of singular patterns in the 1-D Gray-Scott model: a matched asymptotic approach. Physica D , Author: Juncheng Wei, Matthias Winter.

In a more recent paper [8], McGough and Riley used more robust numerical schemes to confirm the results of [11]. Moreover, if Ω is a bounded smooth domain in R n (n ≥ 1), the authors of [8. Stable localized moving patterns in the 2-D Gray-Scott model R. P. Munafo Novem Abstract I show stable, localized, single and multi-spot patterns of three classes { stationary, moving, and rotating {that exist within a limited range of parameter values in the two-dimensional Gray-Scott reaction-di usion model with ˙= D u=D v = 2. Notable here is the NLEP stability analysis of pulses, the SLEP method for spikes, and the study of self-replication of pulses for GS model in 1-D. Rigorous framework in 1-D for 2-spike dynamics for GM model in semi-strong regimebased on renormalization group . The Hopf dance is first recovered by a detailed numerical analysis of the full Busse balloon in an explicit Gray-Scott model. The structure, and its generic nature, is confirmed by a rigorous analysis of singular long wave length patterns in a normal form model for pulse-type solutions in two component, singularly perturbed, reaction-diffusion Cited by: