{"id":"https://openalex.org/W1823752871","doi":"https://doi.org/10.1142/s0218127415501254","title":"Accurate Approximation of Homoclinic Solutions in Gray\u2013Scott Kinetic Model","display_name":"Accurate Approximation of Homoclinic Solutions in Gray\u2013Scott Kinetic Model","publication_year":2015,"publication_date":"2015-08-01","ids":{"openalex":"https://openalex.org/W1823752871","doi":"https://doi.org/10.1142/s0218127415501254","mag":"1823752871"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127415501254","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127415501254","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ris.utwente.nl/ws/files/6864742/S0218127415501254.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007494022","display_name":"Yuri A. Kuznetsov","orcid":"https://orcid.org/0000-0003-2289-0801"},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Yu. A. Kuznetsov","raw_affiliation_strings":["Department of Applied Mathematics, University of Twente, Zilverling Building, P. O. Box 217, 7500AE Enschede, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Twente, Zilverling Building, P. O. Box 217, 7500AE Enschede, The Netherlands","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062882766","display_name":"Hil G. E. Meijer","orcid":"https://orcid.org/0000-0003-1526-3762"},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"H. G. E. Meijer","raw_affiliation_strings":["Department of Applied Mathematics, University of Twente, Zilverling Building, P. O. Box 217, 7500AE Enschede, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Twente, Zilverling Building, P. O. Box 217, 7500AE Enschede, The Netherlands","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052821015","display_name":"Bashir Al\u2010Hdaibat","orcid":"https://orcid.org/0000-0003-1846-7410"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"B. Al-Hdaibat","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, 9000 Gent, Belgium","Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), 9000 Gent, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, 9000 Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), 9000 Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067569718","display_name":"W. Govaerts","orcid":"https://orcid.org/0000-0002-1081-6252"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"W. Govaerts","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, 9000 Gent, Belgium","Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), 9000 Gent, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, 9000 Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), 9000 Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8361,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.87891988,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"25","issue":"09","first_page":"1550125","last_page":"1550125"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.9741795063018799},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.8940879106521606},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.690704345703125},{"id":"https://openalex.org/keywords/numerical-continuation","display_name":"Numerical continuation","score":0.6248518824577332},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6152395606040955},{"id":"https://openalex.org/keywords/bogdanov\u2013takens-bifurcation","display_name":"Bogdanov\u2013Takens bifurcation","score":0.6054739952087402},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.596441388130188},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5349752902984619},{"id":"https://openalex.org/keywords/heteroclinic-orbit","display_name":"Heteroclinic orbit","score":0.4954923391342163},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3813779652118683},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.3417740762233734},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1529330313205719},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11212223768234253},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07785835862159729}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9741795063018799},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.8940879106521606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.690704345703125},{"id":"https://openalex.org/C2775978667","wikidata":"https://www.wikidata.org/wiki/Q7069654","display_name":"Numerical continuation","level":4,"score":0.6248518824577332},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6152395606040955},{"id":"https://openalex.org/C22257346","wikidata":"https://www.wikidata.org/wiki/Q4937510","display_name":"Bogdanov\u2013Takens bifurcation","level":5,"score":0.6054739952087402},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.596441388130188},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5349752902984619},{"id":"https://openalex.org/C184481792","wikidata":"https://www.wikidata.org/wiki/Q1992087","display_name":"Heteroclinic orbit","level":5,"score":0.4954923391342163},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3813779652118683},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.3417740762233734},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1529330313205719},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11212223768234253},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07785835862159729},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1142/s0218127415501254","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127415501254","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:ris.utwente.nl:publications/70909173-e400-4ac2-83e9-7fa6e691cccf","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/70909173-e400-4ac2-83e9-7fa6e691cccf","pdf_url":"https://ris.utwente.nl/ws/files/6864742/S0218127415501254.pdf","source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Kouznetsov, I A, Meijer, H G E, Al Hdaibat, B & Govaerts, W 2015, 'Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model', International journal of bifurcation and chaos in applied sciences and engineering, vol. 25, no. 9, pp. 1550125. https://doi.org/10.1142/S0218127415501254","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:archive.ugent.be:6922082","is_oa":false,"landing_page_url":"http://hdl.handle.net/1854/LU-6922082","pdf_url":null,"source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0218-1274","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:ris.utwente.nl:publications/70909173-e400-4ac2-83e9-7fa6e691cccf","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:uu:oai:dspace.library.uu.nl:1874/329540","is_oa":false,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/329540","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 25(9). World Scientific Publishing Co. Pte Ltd","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:ris.utwente.nl:publications/70909173-e400-4ac2-83e9-7fa6e691cccf","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/70909173-e400-4ac2-83e9-7fa6e691cccf","pdf_url":"https://ris.utwente.nl/ws/files/6864742/S0218127415501254.pdf","source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Kouznetsov, I A, Meijer, H G E, Al Hdaibat, B & Govaerts, W 2015, 'Accurate Approximation of Homoclinic Solutions in Gray-Scott Kinetic Model', International journal of bifurcation and chaos in applied sciences and engineering, vol. 25, no. 9, pp. 1550125. https://doi.org/10.1142/S0218127415501254","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1823752871.pdf","grobid_xml":"https://content.openalex.org/works/W1823752871.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1567812234","https://openalex.org/W1592415565","https://openalex.org/W1596321532","https://openalex.org/W2033980468","https://openalex.org/W2052688404","https://openalex.org/W2057456335","https://openalex.org/W2063084778","https://openalex.org/W2066082500","https://openalex.org/W2079371292","https://openalex.org/W2081696580","https://openalex.org/W2082395037","https://openalex.org/W2088827616","https://openalex.org/W2089876099","https://openalex.org/W2480701976","https://openalex.org/W2905382927","https://openalex.org/W4293079168"],"related_works":["https://openalex.org/W2951537815","https://openalex.org/W4299991393","https://openalex.org/W2356323067","https://openalex.org/W944345475","https://openalex.org/W2362555640","https://openalex.org/W2890492950","https://openalex.org/W1673711094","https://openalex.org/W2018102019","https://openalex.org/W2067447470","https://openalex.org/W1823752871"],"abstract_inverted_index":{"The":[0,13,69],"second-order":[1,62],"predictor":[2],"for":[3,64],"the":[4,10,19,22,37,52,65],"homoclinic":[5,23,66],"orbit":[6],"is":[7,15,43],"applied":[8],"to":[9,17,45,58],"Gray\u2013Scott":[11],"model.":[12],"problem":[14],"used":[16],"illustrate":[18],"approximation":[20],"of":[21,33],"orbits":[24],"near":[25],"a":[26,60],"generic":[27],"Bogdanov\u2013Takens":[28,53],"bifurcation":[29,67],"in":[30,51],"n-dimensional":[31],"systems":[32],"differential":[34],"equations.":[35],"In":[36],"process,":[38],"we":[39],"show":[40],"that":[41],"it":[42],"necessary":[44],"take":[46],"(usually":[47],"ignored)":[48],"cubic":[49],"terms":[50],"normal":[54],"form":[55],"into":[56],"account":[57],"derive":[59],"correct":[61],"prediction":[63],"curve.":[68],"analytic":[70],"solutions":[71],"are":[72],"compared":[73],"with":[74],"those":[75],"obtained":[76],"by":[77],"numerical":[78],"continuation.":[79]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}
