2008
DOI: 10.1093/imamat/hxn015
|View full text |Cite
|
Sign up to set email alerts
|

A comparison of periodic travelling wave generation by Robin and Dirichlet boundary conditions in oscillatory reaction-diffusion equations

Abstract: Periodic travelling waves are an important solution form in oscillatory reaction-diffusion equations. I have shown previously that such waves arise naturally near a boundary at which a Dirichlet condition is applied. This result has applications in ecology, providing a potential explanation for the periodic waves seen in a number of natural populations. However, in ecological applications the Dirichlet boundary condition typically arises as a simple approximation to a more realistic Robin condition. In this pa… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

0
5
0

Year Published

2010
2010
2022
2022

Publication Types

Select...
8

Relationship

0
8

Authors

Journals

citations
Cited by 15 publications
(5 citation statements)
references
References 57 publications
0
5
0
Order By: Relevance
“…This is a standard approximation in biology applications (see [11] for instance). To justify the boundary condition, consider as an illustration the one-dimensional case, with a wound domain Ω = [0, L], L > 0.…”
Section: Inflammatory Macrophagesmentioning
confidence: 99%
“…This is a standard approximation in biology applications (see [11] for instance). To justify the boundary condition, consider as an illustration the one-dimensional case, with a wound domain Ω = [0, L], L > 0.…”
Section: Inflammatory Macrophagesmentioning
confidence: 99%
“…PTWs are often observed in ecological systems (Sherratt 2008 ) and were the focus of works that discussed their potential drivers (Kaitala and Ranta 1998 ; Petrovskii and Malchow 1999 ). As PTWs are an inherently spatial phenomena, it is natural to ask what are the implications of landscape alterations for such spatiotemporal dynamics.…”
Section: Discussionmentioning
confidence: 99%
“…be approximated by h = 0, and this approximation is in widespread use. In fact, I have shown previously [36] that, for PTW generation, the Robin condition is particularly well approximated by the Dirichlet condition, which I will use throughout this paper. Figure 1a illustrates a typical solution of (2.1) for C > C Hopf , on a large domain with h = p = 0 at the left-hand (hostile) boundary and the zero-flux condition ∂p/∂x = ∂h/∂x = 0 at the other boundary.…”
Section: Boundary-generated Periodic Travelling Waves In Predator-prey Systemsmentioning
confidence: 99%