Basin of Attraction of Solutions with Pattern Formation in Slow-Fast Reaction-Diffusion Systems.
Identifieur interne : 000050 ( PubMed/Checkpoint ); précédent : 000049; suivant : 000051Basin of Attraction of Solutions with Pattern Formation in Slow-Fast Reaction-Diffusion Systems.
Auteurs : B. Ambrosio [France] ; M A Aziz-Alaoui [France]Source :
- Acta biotheoretica [ 1572-8358 ] ; 2016.
Abstract
This article is devoted to the characterization of the basin of attraction of pattern solutions for some slow-fast reaction-diffusion systems with a symmetric property and an underlying oscillatory reaction part. We characterize some subsets of initial conditions that prevent the dynamical system to evolve asymptotically toward solutions which are homogeneous in space. We also perform numerical simulations that illustrate theoretical results and give rise to symmetric and non-symmetric pattern solutions. We obtain these last solutions by choosing particular random initial conditions.
DOI: 10.1007/s10441-016-9294-z
PubMed: 27770317
Affiliations:
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Ambrosio</name><affiliation wicri:level="3"><nlm:affiliation>UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, Normandie Univ, 76600, Le Havre, France. benjamin.ambrosio@univ-lehavre.fr.</nlm:affiliation><country xml:lang="fr">France</country><wicri:regionArea>UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, Normandie Univ, 76600, Le Havre</wicri:regionArea><placeName><region type="region" nuts="2">Région Normandie</region><region type="old region" nuts="2">Haute-Normandie</region><settlement type="city">Le Havre</settlement></placeName></affiliation></author><author><name sortKey="Aziz Alaoui, M A" sort="Aziz Alaoui, M A" uniqKey="Aziz Alaoui M" first="M A" last="Aziz-Alaoui">M A Aziz-Alaoui</name><affiliation wicri:level="3"><nlm:affiliation>UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, Normandie Univ, 76600, Le Havre, France.</nlm:affiliation><country xml:lang="fr">France</country><wicri:regionArea>UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, Normandie Univ, 76600, Le Havre</wicri:regionArea><placeName><region type="region" nuts="2">Région Normandie</region><region type="old region" nuts="2">Haute-Normandie</region><settlement type="city">Le Havre</settlement></placeName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PubMed</idno><date when="2016">2016</date><idno type="RBID">pubmed:27770317</idno><idno type="pmid">27770317</idno><idno type="doi">10.1007/s10441-016-9294-z</idno><idno type="wicri:Area/PubMed/Corpus">000005</idno><idno type="wicri:Area/PubMed/Curation">000005</idno><idno type="wicri:Area/PubMed/Checkpoint">000005</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Basin of Attraction of Solutions with Pattern Formation in Slow-Fast Reaction-Diffusion Systems.</title><author><name sortKey="Ambrosio, B" sort="Ambrosio, B" uniqKey="Ambrosio B" first="B" last="Ambrosio">B. Ambrosio</name><affiliation wicri:level="3"><nlm:affiliation>UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, Normandie Univ, 76600, Le Havre, France. benjamin.ambrosio@univ-lehavre.fr.</nlm:affiliation><country xml:lang="fr">France</country><wicri:regionArea>UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, Normandie Univ, 76600, Le Havre</wicri:regionArea><placeName><region type="region" nuts="2">Région Normandie</region><region type="old region" nuts="2">Haute-Normandie</region><settlement type="city">Le Havre</settlement></placeName></affiliation></author><author><name sortKey="Aziz Alaoui, M A" sort="Aziz Alaoui, M A" uniqKey="Aziz Alaoui M" first="M A" last="Aziz-Alaoui">M A Aziz-Alaoui</name><affiliation wicri:level="3"><nlm:affiliation>UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, Normandie Univ, 76600, Le Havre, France.</nlm:affiliation><country xml:lang="fr">France</country><wicri:regionArea>UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, Normandie Univ, 76600, Le Havre</wicri:regionArea><placeName><region type="region" nuts="2">Région Normandie</region><region type="old region" nuts="2">Haute-Normandie</region><settlement type="city">Le Havre</settlement></placeName></affiliation></author></analytic><series><title level="j">Acta biotheoretica</title><idno type="eISSN">1572-8358</idno><imprint><date when="2016" type="published">2016</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">This article is devoted to the characterization of the basin of attraction of pattern solutions for some slow-fast reaction-diffusion systems with a symmetric property and an underlying oscillatory reaction part. We characterize some subsets of initial conditions that prevent the dynamical system to evolve asymptotically toward solutions which are homogeneous in space. We also perform numerical simulations that illustrate theoretical results and give rise to symmetric and non-symmetric pattern solutions. We obtain these last solutions by choosing particular random initial conditions.</div></front></TEI><pubmed><MedlineCitation Status="Publisher" Owner="NLM"><PMID Version="1">27770317</PMID><DateCreated><Year>2016</Year><Month>10</Month><Day>22</Day></DateCreated><DateRevised><Year>2016</Year><Month>10</Month><Day>23</Day></DateRevised><Article PubModel="Print-Electronic"><Journal><ISSN IssnType="Electronic">1572-8358</ISSN><JournalIssue CitedMedium="Internet"><PubDate><Year>2016</Year><Month>Oct</Month><Day>21</Day></PubDate></JournalIssue><Title>Acta biotheoretica</Title><ISOAbbreviation>Acta Biotheor.</ISOAbbreviation></Journal><ArticleTitle>Basin of Attraction of Solutions with Pattern Formation in Slow-Fast Reaction-Diffusion Systems.</ArticleTitle><Pagination><MedlinePgn></MedlinePgn></Pagination><Abstract><AbstractText NlmCategory="UNASSIGNED">This article is devoted to the characterization of the basin of attraction of pattern solutions for some slow-fast reaction-diffusion systems with a symmetric property and an underlying oscillatory reaction part. We characterize some subsets of initial conditions that prevent the dynamical system to evolve asymptotically toward solutions which are homogeneous in space. We also perform numerical simulations that illustrate theoretical results and give rise to symmetric and non-symmetric pattern solutions. We obtain these last solutions by choosing particular random initial conditions.</AbstractText></Abstract><AuthorList CompleteYN="Y"><Author ValidYN="Y"><LastName>Ambrosio</LastName><ForeName>B</ForeName><Initials>B</Initials><AffiliationInfo><Affiliation>UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, Normandie Univ, 76600, Le Havre, France. benjamin.ambrosio@univ-lehavre.fr.</Affiliation></AffiliationInfo></Author><Author ValidYN="Y"><LastName>Aziz-Alaoui</LastName><ForeName>M A</ForeName><Initials>MA</Initials><AffiliationInfo><Affiliation>UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, Normandie Univ, 76600, Le Havre, France.</Affiliation></AffiliationInfo></Author></AuthorList><Language>ENG</Language><PublicationTypeList><PublicationType UI="">JOURNAL ARTICLE</PublicationType></PublicationTypeList><ArticleDate DateType="Electronic"><Year>2016</Year><Month>Oct</Month><Day>21</Day></ArticleDate></Article><MedlineJournalInfo><Country>Netherlands</Country><MedlineTA>Acta Biotheor</MedlineTA><NlmUniqueID>0421520</NlmUniqueID><ISSNLinking>0001-5342</ISSNLinking></MedlineJournalInfo><KeywordList Owner="NOTNLM"><Keyword MajorTopicYN="N">FitzHugh–Nagumo</Keyword><Keyword MajorTopicYN="N">Limit-cycles</Keyword><Keyword MajorTopicYN="N">Pattern formation</Keyword><Keyword MajorTopicYN="N">Reaction diffusion systems</Keyword><Keyword MajorTopicYN="N">Slow–fast analysis</Keyword></KeywordList></MedlineCitation><PubmedData><History><PubMedPubDate PubStatus="received"><Year>2016</Year><Month>1</Month><Day>5</Day></PubMedPubDate><PubMedPubDate PubStatus="accepted"><Year>2016</Year><Month>10</Month><Day>11</Day></PubMedPubDate><PubMedPubDate PubStatus="pubmed"><Year>2016</Year><Month>10</Month><Day>23</Day><Hour>6</Hour><Minute>0</Minute></PubMedPubDate><PubMedPubDate PubStatus="medline"><Year>2016</Year><Month>10</Month><Day>23</Day><Hour>6</Hour><Minute>0</Minute></PubMedPubDate><PubMedPubDate PubStatus="entrez"><Year>2016</Year><Month>10</Month><Day>23</Day><Hour>6</Hour><Minute>0</Minute></PubMedPubDate></History><PublicationStatus>aheadofprint</PublicationStatus><ArticleIdList><ArticleId IdType="pubmed">27770317</ArticleId><ArticleId IdType="doi">10.1007/s10441-016-9294-z</ArticleId><ArticleId IdType="pii">10.1007/s10441-016-9294-z</ArticleId></ArticleIdList></PubmedData></pubmed><affiliations><list><country><li>France</li></country><region><li>Haute-Normandie</li><li>Région Normandie</li></region><settlement><li>Le Havre</li></settlement></list><tree><country name="France"><region name="Région Normandie"><name sortKey="Ambrosio, B" sort="Ambrosio, B" uniqKey="Ambrosio B" first="B" last="Ambrosio">B. Ambrosio</name></region><name sortKey="Aziz Alaoui, M A" sort="Aziz Alaoui, M A" uniqKey="Aziz Alaoui M" first="M A" last="Aziz-Alaoui">M A Aziz-Alaoui</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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