{"id":"https://openalex.org/W2789596271","doi":"https://doi.org/10.4236/jamp.2018.63049","title":"High Order Boundary Conditions Technique for the Computation of Global Homoclinic Bifurcation","display_name":"High Order Boundary Conditions Technique for the Computation of Global Homoclinic Bifurcation","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2789596271","doi":"https://doi.org/10.4236/jamp.2018.63049","mag":"2789596271"},"language":"en","primary_location":{"id":"doi:10.4236/jamp.2018.63049","doi":"https://doi.org/10.4236/jamp.2018.63049","is_oa":true,"landing_page_url":"https://doi.org/10.4236/jamp.2018.63049","pdf_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=83231","source":{"id":"https://openalex.org/S2764580047","display_name":"Journal of Applied Mathematics and Physics","issn_l":"2327-4352","issn":["2327-4352","2327-4379"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Physics","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2789596271"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=83231","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011128060","display_name":"Panagiotis S. Douris","orcid":"https://orcid.org/0000-0002-1234-6469","observed_orcids":["https://orcid.org/0000-0002-1234-6469"]},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Panagiotis S. Douris","raw_affiliation_strings":["Department of Electrical & Computer Engineering, University of Patras, Patras, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical & Computer Engineering, University of Patras, Patras, Greece","institution_ids":["https://openalex.org/I174878644"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049079299","display_name":"Michail P. Markakis","orcid":"https://orcid.org/0000-0001-7762-8339","observed_orcids":["https://orcid.org/0000-0001-7762-8339"]},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Michail P. Markakis","raw_affiliation_strings":["Department of Electrical & Computer Engineering, University of Patras, Patras, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical & Computer Engineering, University of Patras, Patras, Greece","institution_ids":["https://openalex.org/I174878644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049079299"],"corresponding_institution_ids":["https://openalex.org/I174878644"],"apc_list":null,"apc_paid":null,"fwci":0.3721,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.46636597,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"06","issue":"03","first_page":"554","last_page":"572"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.6366999745368958,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.6366999745368958,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.14249999821186066,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.04969999939203262,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"homoclinic bifurcation","score":0.9309999942779541},{"id":"https://openalex.org/keywords/global-bifurcation","display_name":"global bifurcation","score":0.7039999961853027},{"id":"https://openalex.org/keywords/high-order-boundary-conditions","display_name":"high-order boundary conditions","score":0.906000018119812},{"id":"https://openalex.org/keywords/orthogonal-collocation-on-finite-elements","display_name":"orthogonal collocation on finite elements","score":0.9670000076293945}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.8476590514183044},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.7052183151245117},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6226735711097717},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6108344197273254},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.599177360534668},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5927600860595703},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5751564502716064},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5514366626739502},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5488505959510803},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5351657867431641},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4910314083099365},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4321174621582031},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.41493335366249084},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40559566020965576},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3403310179710388},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2206512689590454},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17699798941612244},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.16515636444091797},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07739719748497009},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4236/jamp.2018.63049","doi":"https://doi.org/10.4236/jamp.2018.63049","is_oa":true,"landing_page_url":"https://doi.org/10.4236/jamp.2018.63049","pdf_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=83231","source":{"id":"https://openalex.org/S2764580047","display_name":"Journal of Applied Mathematics and Physics","issn_l":"2327-4352","issn":["2327-4352","2327-4379"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Physics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4236/jamp.2018.63049","doi":"https://doi.org/10.4236/jamp.2018.63049","is_oa":true,"landing_page_url":"https://doi.org/10.4236/jamp.2018.63049","pdf_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=83231","source":{"id":"https://openalex.org/S2764580047","display_name":"Journal of Applied Mathematics and Physics","issn_l":"2327-4352","issn":["2327-4352","2327-4379"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Physics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2789596271.pdf","grobid_xml":"https://content.openalex.org/works/W2789596271.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1971808848","https://openalex.org/W1973222707","https://openalex.org/W1989097268","https://openalex.org/W2033980468","https://openalex.org/W2036350807","https://openalex.org/W2040891655","https://openalex.org/W2068324320","https://openalex.org/W2089876099","https://openalex.org/W2091534537","https://openalex.org/W2141394518","https://openalex.org/W2169070947","https://openalex.org/W3025401191"],"related_works":["https://openalex.org/W1532361234","https://openalex.org/W7067801254","https://openalex.org/W1982449011","https://openalex.org/W2560474658","https://openalex.org/W2091534537","https://openalex.org/W2015923726","https://openalex.org/W2076394902","https://openalex.org/W2948873932","https://openalex.org/W2019833761","https://openalex.org/W2091005094"],"abstract_inverted_index":{"In":[0,58],"the":[1,9,22,54,62,66,87,96,104,108],"present":[2],"paper,":[3],"a":[4,38],"custom":[5],"algorithm":[6,98],"based":[7],"on":[8,14],"method":[10],"of":[11,24,33,41,53,68,86,95,103],"orthogonal":[12],"collocation":[13],"finite":[15],"elements":[16],"is":[17,71,99],"presented":[18],"and":[19,83,107],"used":[20,84],"for":[21],"location":[23,67],"global":[25,34],"homoclinic":[26],"point-to-point":[27],"asymptotic":[28],"connecting":[29],"orbits.":[30],"This":[31],"kind":[32],"bifurcation":[35],"occurs":[36],"in":[37,43],"large":[39],"variety":[40],"problems":[42],"Applied":[44],"Sciences,":[45],"being":[46],"associated":[47],"to":[48,60],"specific,":[49],"significant":[50],"physical":[51],"aspects":[52],"problem":[55],"under":[56],"consideration.":[57],"order":[59,74,81,91],"confront":[61],"difficulties":[63],"faced":[64],"when":[65],"such":[69],"orbits":[70],"attempted,":[72],"high":[73],"boundary":[75],"conditions":[76],"are":[77],"constructed":[78],"through":[79],"scale":[80],"approximations,":[82],"instead":[85],"more":[88],"common":[89],"first":[90],"ones.":[92],"The":[93],"effectiveness":[94],"implemented":[97],"justified":[100],"by":[101],"means":[102],"specific":[105],"applications":[106],"figures":[109],"presented.":[110]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2018-03-29T00:00:00"}