A Nonlocal Eigenvalue Problem and the Stability of Spikes for Reaction–Diffusion Systems with Fractional Reaction Rates-Reference-Cited by-同舟云学术

A Nonlocal Eigenvalue Problem and the Stability of Spikes for Reaction–Diffusion Systems with Fractional Reaction Rates

Published:2003-06 Issue:06 Volume:13 Page:1529-1543
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Wei Juncheng¹,Winter Matthias²

Affiliation:

1. Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong

2. Mathematisches Institut, Universität Stuttgart, D-70511 Stuttgart, Germany

Abstract

We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction–diffusion systems with fractional reaction rates such as the Sel'kov model, the Gray–Scott system, the hypercycle of Eigen and Schuster, angiogenesis, and the generalized Gierer–Meinhardt system. We give some sufficient and explicit conditions for stability by studying the corresponding nonlocal eigenvalue problem in a new range of parameters.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127403007369

Reference30 articles.

1. A priori bounds and global existence of solutions of the steady-state Sel'kov model

2. Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach

3. Large stable pulse solutions in reaction-diffusion equations

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Cops-on-the-dots: The linear stability of crime hotspots for a 1-D reaction-diffusion model of urban crime;European Journal of Applied Mathematics;2019-11-11

2. Existence, Stability, and Dynamics of Ring and Near-Ring Solutions to the Saturated Gierer--Meinhardt Model in the Semistrong Regime;SIAM Journal on Applied Dynamical Systems;2017-01

3. Reaction-Diffusion Systems with Many Components;Mathematical Aspects of Pattern Formation in Biological Systems;2014

4. The Nonlocal Eigenvalue Problem (NLEP);Mathematical Aspects of Pattern Formation in Biological Systems;2014

5. Approximately invariant manifolds and global dynamics of spike states;Inventiones mathematicae;2008-07-08