The Effect of Geometry on Survival and Extinction in a Moving-Boundary Problem Motivated by the Fisher-KPP Equation
Clicks: 86
ID: 282515
2022
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This
article has not been analysed, so there is no overall score —
reader engagement is measured and shown alongside.
Reader Engagement
Steady Performance
25.5
/100
86 views
33 readers
AI Quality Assessment
Not analyzed
Readership in this journal
SteadyRanked #213 of 803 articles by views in arXiv
Most read
Least read
Bar heights use a square-root scale. Only the 120 most-read articles are drawn; the journal has 803 in total.
Mint this article as an NFT
Not yet mintedCreate a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.
5
SUSD
one-off · no wallet required
Abstract
The Fisher-Stefan model involves solving the Fisher-KPP equation on a domain
whose boundary evolves according to a Stefan-like condition. The Fisher-Stefan
model alleviates two practical limitations of the standard Fisher-KPP model
when applied to biological invasion. First, unlike the Fisher-KPP equation,
solutions to the Fisher-Stefan model have compact support, enabling one to
define the interface between occupied and unoccupied regions unambiguously.
Second, the Fisher-Stefan model admits solutions for which the population
becomes extinct, which is not possible in the Fisher-KPP equation. Previous
research showed that population survival or extinction in the Fisher-Stefan
model depends on a critical length in one-dimensional Cartesian or
radially-symmetric geometry. However, the survival and extinction behaviour for
general two-dimensional regions remains unexplored. We combine analysis and
level-set numerical simulations of the Fisher-Stefan model to investigate the
survival-extinction conditions for rectangular-shaped initial conditions. We
show that it is insufficient to generalise the critical length conditions to
critical area in two-dimensions. Instead, knowledge of the region geometry is
required to determine whether a population will survive or become extinct.
| Reference Key |
simpson2022the
Use this key to autocite in the manuscript while using
SciMatic Manuscript Manager or Thesis Manager
|
|---|---|
| Authors | Alexander K. Y. Tam; Matthew J. Simpson |
| Journal | arXiv |
| Year | 2022 |
| DOI |
DOI not found
|
| URL | |
| Keywords |
Citations
No citations found. To add a citation, contact the admin at info@scimatic.org
Comments
No comments yet. Be the first to comment on this article.