scholarly journals Existence of multi-peak solutions to the Schnakenberg model with heterogeneity on metric graphs

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yuta Ishii ◽  
Kazuhiro Kurata
Keyword(s):  
Metric Graphs ◽  
Schnakenberg Model

scholarly journals On the nonlinear Dirac equation on noncompact metric graphs

2021 ◽  
Vol 278 ◽  
pp. 326-357
Author(s):  
William Borrelli ◽  
Raffaele Carlone ◽  
Lorenzo Tentarelli
Keyword(s):  
Dirac Equation ◽  
Metric Graphs ◽  
Nonlinear Dirac Equation

scholarly journals Stabilizing a homoclinic stripe

2018 ◽  
Vol 376 (2135) ◽  
pp. 20180110 ◽  
Author(s):  
Theodore Kolokolnikov ◽  
Michael Ward ◽  
Justin Tzou ◽  
Juncheng Wei
Keyword(s):  
Reaction Diffusion ◽  
Dissipative Structures ◽  
Vegetation Patterns ◽  
Theme Issue ◽  
One Dimensional ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Schnakenberg Model ◽  
Break Up ◽  
Variable Substrate

For a large class of reaction–diffusion systems with large diffusivity ratio, it is well known that a two-dimensional stripe (whose cross-section is a one-dimensional homoclinic spike) is unstable and breaks up into spots. Here, we study two effects that can stabilize such a homoclinic stripe. First, we consider the addition of anisotropy to the model. For the Schnakenberg model, we show that (an infinite) stripe can be stabilized if the fast-diffusing variable (substrate) is sufficiently anisotropic. Two types of instability thresholds are derived: zigzag (or bending) and break-up instabilities. The instability boundaries subdivide parameter space into three distinct zones: stable stripe, unstable stripe due to bending and unstable due to break-up instability. Numerical experiments indicate that the break-up instability is supercritical leading to a ‘spotted-stripe’ solution. Finally, we perform a similar analysis for the Klausmeier model of vegetation patterns on a steep hill, and examine transition from spots to stripes. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

scholarly journals Pattern formation of a coupled two-cell Schnakenberg model

2017 ◽  
Vol 10 (5) ◽  
pp. 1051-1062
Author(s):  
Guanqi Liu ◽  
◽  
Yuwen Wang ◽  
Keyword(s):  
Pattern Formation ◽  
Schnakenberg Model

scholarly journals Heat kernels on metric graphs and a trace formula

2007 ◽  
pp. 175-198 ◽  
Author(s):  
Vadim Kostrykin ◽  
Jürgen Potthoff ◽  
Robert Schrader
Keyword(s):  
Trace Formula ◽  
Heat Kernels ◽  
Metric Graphs

Approximation Algorithms for the Star k-Hub Center Problem in Metric Graphs

2016 ◽  
pp. 222-234 ◽  
Author(s):  
Li-Hsuan Chen ◽  
Dun-Wei Cheng ◽  
Sun-Yuan Hsieh ◽  
Ling-Ju Hung ◽  
Chia-Wei Lee ◽  
...  
Keyword(s):  
Approximation Algorithms ◽  
Center Problem ◽  
Metric Graphs
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