Journal article 114 views 31 downloads
Weakly nonlinear analysis of a two-species non-local advection–diffusion system
Nonlinear Analysis: Real World Applications, Volume: 78, Start page: 104086
Swansea University Author:
Valeria Giunta
-
PDF | Version of Record
©2024 TheAuthors. This is an open access article under the CC BY license
Download (1.44MB)
DOI (Published version): 10.1016/j.nonrwa.2024.104086
Abstract
Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection–diffusion model with nonlocal advection terms describing the species movements generated by inter-species interactions....
Published in: | Nonlinear Analysis: Real World Applications |
---|---|
ISSN: | 1468-1218 |
Published: |
Elsevier BV
2024
|
Online Access: |
Check full text
|
URI: | https://cronfa.swan.ac.uk/Record/cronfa64703 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
first_indexed |
2023-10-10T11:26:55Z |
---|---|
last_indexed |
2023-10-10T11:26:55Z |
id |
cronfa64703 |
recordtype |
SURis |
fullrecord |
<?xml version="1.0" encoding="utf-8"?><rfc1807 xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema"><bib-version>v2</bib-version><id>64703</id><entry>2023-10-10</entry><title>Weakly nonlinear analysis of a two-species non-local advection–diffusion system</title><swanseaauthors><author><sid>50456cce4b2c7be66f8302d418963b0c</sid><ORCID>0000-0003-1156-7136</ORCID><firstname>Valeria</firstname><surname>Giunta</surname><name>Valeria Giunta</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2023-10-10</date><deptcode>SMA</deptcode><abstract>Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection–diffusion model with nonlocal advection terms describing the species movements generated by inter-species interactions. We use linear analysis to assess the stability of the constant steady state, then weakly nonlinear analysis to recover the shape and stability of non-homogeneous solutions. Since the system arises from a conservation law, the resulting amplitude equations consist of a Ginzburg–Landau equation coupled with an equation for the zero mode. In particular, this means that supercritical branches from the Ginzburg–Landau equation need not be stable. Indeed, we find that, depending on the parameters, bifurcations can be subcritical (always unstable), stable supercritical, or unstable supercritical. We show numerically that, when small amplitude patterns are unstable, the system exhibits large amplitude patterns and hysteresis, even in supercritical regimes. Finally, we construct bifurcation diagrams by combining our analysis with a previous study of the minimizers of the associated energy functional. Through this approach we reveal parameter regions in which stable small amplitude patterns coexist with strongly modulated solutions.</abstract><type>Journal Article</type><journal>Nonlinear Analysis: Real World Applications</journal><volume>78</volume><journalNumber/><paginationStart>104086</paginationStart><paginationEnd/><publisher>Elsevier BV</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>1468-1218</issnPrint><issnElectronic/><keywords>Nonlocal interactions; Pattern formation; Amplitude equation formalism; Bifurcations; Multi-stability</keywords><publishedDay>23</publishedDay><publishedMonth>2</publishedMonth><publishedYear>2024</publishedYear><publishedDate>2024-02-23</publishedDate><doi>10.1016/j.nonrwa.2024.104086</doi><url/><notes/><college>COLLEGE NANME</college><department>Mathematics</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SMA</DepartmentCode><institution>Swansea University</institution><apcterm>SU Library paid the OA fee (TA Institutional Deal)</apcterm><funders>JRP and VG acknowledge support of Engineering and Physical Sciences Research Council (EPSRC) grant EP/V002988/1 awarded to JRP. VG is also grateful for support from the National Group of Mathematical Physics (GNFM-INdAM). TH is supported through a discovery grant of the Natural Science and Engineering Research Council of Canada (NSERC), RGPIN-2017-04158. MAL gratefully acknowledges support from NSERC Discovery Grant RGPIN-2018-05210 and from the Gilbert and Betty Kennedy Chair in Mathematical Biology.</funders><projectreference/><lastEdited>2024-03-01T15:28:33.4802469</lastEdited><Created>2023-10-10T12:25:17.6855997</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Valeria</firstname><surname>Giunta</surname><orcid>0000-0003-1156-7136</orcid><order>1</order></author><author><firstname>Thomas</firstname><surname>Hillen</surname><order>2</order></author><author><firstname>Mark A.</firstname><surname>Lewis</surname><order>3</order></author><author><firstname>Jonathan R.</firstname><surname>Potts</surname><order>4</order></author></authors><documents><document><filename>64703__29610__8f4f1a915d7144af92da3055534b78a7.pdf</filename><originalFilename>64703_VoR.pdf</originalFilename><uploaded>2024-03-01T15:26:58.3159687</uploaded><type>Output</type><contentLength>1510262</contentLength><contentType>application/pdf</contentType><version>Version of Record</version><cronfaStatus>true</cronfaStatus><documentNotes>©2024 TheAuthors. This is an open access article under the CC BY license</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language><licence>http://creativecommons.org/licenses/by/4.0/</licence></document></documents><OutputDurs/></rfc1807> |
spelling |
v2 64703 2023-10-10 Weakly nonlinear analysis of a two-species non-local advection–diffusion system 50456cce4b2c7be66f8302d418963b0c 0000-0003-1156-7136 Valeria Giunta Valeria Giunta true false 2023-10-10 SMA Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection–diffusion model with nonlocal advection terms describing the species movements generated by inter-species interactions. We use linear analysis to assess the stability of the constant steady state, then weakly nonlinear analysis to recover the shape and stability of non-homogeneous solutions. Since the system arises from a conservation law, the resulting amplitude equations consist of a Ginzburg–Landau equation coupled with an equation for the zero mode. In particular, this means that supercritical branches from the Ginzburg–Landau equation need not be stable. Indeed, we find that, depending on the parameters, bifurcations can be subcritical (always unstable), stable supercritical, or unstable supercritical. We show numerically that, when small amplitude patterns are unstable, the system exhibits large amplitude patterns and hysteresis, even in supercritical regimes. Finally, we construct bifurcation diagrams by combining our analysis with a previous study of the minimizers of the associated energy functional. Through this approach we reveal parameter regions in which stable small amplitude patterns coexist with strongly modulated solutions. Journal Article Nonlinear Analysis: Real World Applications 78 104086 Elsevier BV 1468-1218 Nonlocal interactions; Pattern formation; Amplitude equation formalism; Bifurcations; Multi-stability 23 2 2024 2024-02-23 10.1016/j.nonrwa.2024.104086 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University SU Library paid the OA fee (TA Institutional Deal) JRP and VG acknowledge support of Engineering and Physical Sciences Research Council (EPSRC) grant EP/V002988/1 awarded to JRP. VG is also grateful for support from the National Group of Mathematical Physics (GNFM-INdAM). TH is supported through a discovery grant of the Natural Science and Engineering Research Council of Canada (NSERC), RGPIN-2017-04158. MAL gratefully acknowledges support from NSERC Discovery Grant RGPIN-2018-05210 and from the Gilbert and Betty Kennedy Chair in Mathematical Biology. 2024-03-01T15:28:33.4802469 2023-10-10T12:25:17.6855997 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Valeria Giunta 0000-0003-1156-7136 1 Thomas Hillen 2 Mark A. Lewis 3 Jonathan R. Potts 4 64703__29610__8f4f1a915d7144af92da3055534b78a7.pdf 64703_VoR.pdf 2024-03-01T15:26:58.3159687 Output 1510262 application/pdf Version of Record true ©2024 TheAuthors. This is an open access article under the CC BY license true eng http://creativecommons.org/licenses/by/4.0/ |
title |
Weakly nonlinear analysis of a two-species non-local advection–diffusion system |
spellingShingle |
Weakly nonlinear analysis of a two-species non-local advection–diffusion system Valeria Giunta |
title_short |
Weakly nonlinear analysis of a two-species non-local advection–diffusion system |
title_full |
Weakly nonlinear analysis of a two-species non-local advection–diffusion system |
title_fullStr |
Weakly nonlinear analysis of a two-species non-local advection–diffusion system |
title_full_unstemmed |
Weakly nonlinear analysis of a two-species non-local advection–diffusion system |
title_sort |
Weakly nonlinear analysis of a two-species non-local advection–diffusion system |
author_id_str_mv |
50456cce4b2c7be66f8302d418963b0c |
author_id_fullname_str_mv |
50456cce4b2c7be66f8302d418963b0c_***_Valeria Giunta |
author |
Valeria Giunta |
author2 |
Valeria Giunta Thomas Hillen Mark A. Lewis Jonathan R. Potts |
format |
Journal article |
container_title |
Nonlinear Analysis: Real World Applications |
container_volume |
78 |
container_start_page |
104086 |
publishDate |
2024 |
institution |
Swansea University |
issn |
1468-1218 |
doi_str_mv |
10.1016/j.nonrwa.2024.104086 |
publisher |
Elsevier BV |
college_str |
Faculty of Science and Engineering |
hierarchytype |
|
hierarchy_top_id |
facultyofscienceandengineering |
hierarchy_top_title |
Faculty of Science and Engineering |
hierarchy_parent_id |
facultyofscienceandengineering |
hierarchy_parent_title |
Faculty of Science and Engineering |
department_str |
School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics |
document_store_str |
1 |
active_str |
0 |
description |
Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection–diffusion model with nonlocal advection terms describing the species movements generated by inter-species interactions. We use linear analysis to assess the stability of the constant steady state, then weakly nonlinear analysis to recover the shape and stability of non-homogeneous solutions. Since the system arises from a conservation law, the resulting amplitude equations consist of a Ginzburg–Landau equation coupled with an equation for the zero mode. In particular, this means that supercritical branches from the Ginzburg–Landau equation need not be stable. Indeed, we find that, depending on the parameters, bifurcations can be subcritical (always unstable), stable supercritical, or unstable supercritical. We show numerically that, when small amplitude patterns are unstable, the system exhibits large amplitude patterns and hysteresis, even in supercritical regimes. Finally, we construct bifurcation diagrams by combining our analysis with a previous study of the minimizers of the associated energy functional. Through this approach we reveal parameter regions in which stable small amplitude patterns coexist with strongly modulated solutions. |
published_date |
2024-02-23T15:28:29Z |
_version_ |
1792338201653805056 |
score |
11.021648 |