{"id":"https://openalex.org/W2051721023","doi":"https://doi.org/10.1137/070695800","title":"Snaking of Multiple Homoclinic Orbits in Reversible Systems","display_name":"Snaking of Multiple Homoclinic Orbits in Reversible Systems","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2051721023","doi":"https://doi.org/10.1137/070695800","mag":"2051721023"},"language":"en","primary_location":{"id":"doi:10.1137/070695800","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070695800","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007668496","display_name":"J\u00fcrgen Knobloch","orcid":"https://orcid.org/0000-0001-6868-0055"},"institutions":[{"id":"https://openalex.org/I119449181","display_name":"Technische Universit\u00e4t Ilmenau","ror":"https://ror.org/01weqhp73","country_code":"DE","type":"education","lineage":["https://openalex.org/I119449181"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"J. Knobloch","raw_affiliation_strings":["Technische Universit\u00e4t Ilmenau"],"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Ilmenau","institution_ids":["https://openalex.org/I119449181"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074658644","display_name":"Thomas Wagenknecht","orcid":null},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"T. Wagenknecht","raw_affiliation_strings":["University of Manchester\u00a0"],"affiliations":[{"raw_affiliation_string":"University of Manchester\u00a0","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007668496"],"corresponding_institution_ids":["https://openalex.org/I119449181"],"apc_list":null,"apc_paid":null,"fwci":2.8104,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.90411288,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"7","issue":"4","first_page":"1397","last_page":"1420"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9991000294685364,"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/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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.9860489368438721},{"id":"https://openalex.org/keywords/heteroclinic-cycle","display_name":"Heteroclinic cycle","score":0.9209941625595093},{"id":"https://openalex.org/keywords/heteroclinic-orbit","display_name":"Heteroclinic orbit","score":0.6717134714126587},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.6679675579071045},{"id":"https://openalex.org/keywords/heteroclinic-bifurcation","display_name":"Heteroclinic bifurcation","score":0.6088536977767944},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5375912189483643},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.5239952802658081},{"id":"https://openalex.org/keywords/mirroring","display_name":"Mirroring","score":0.5148500800132751},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.5127331018447876},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.5101609230041504},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.435294508934021},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.36785024404525757},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3314499855041504},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3006932735443115},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.20718419551849365},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.07128223776817322}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9860489368438721},{"id":"https://openalex.org/C142115181","wikidata":"https://www.wikidata.org/wiki/Q16948232","display_name":"Heteroclinic cycle","level":5,"score":0.9209941625595093},{"id":"https://openalex.org/C184481792","wikidata":"https://www.wikidata.org/wiki/Q1992087","display_name":"Heteroclinic orbit","level":5,"score":0.6717134714126587},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.6679675579071045},{"id":"https://openalex.org/C73888704","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Heteroclinic bifurcation","level":5,"score":0.6088536977767944},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5375912189483643},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.5239952802658081},{"id":"https://openalex.org/C189645446","wikidata":"https://www.wikidata.org/wiki/Q350865","display_name":"Mirroring","level":2,"score":0.5148500800132751},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5127331018447876},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.5101609230041504},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.435294508934021},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.36785024404525757},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3314499855041504},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3006932735443115},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.20718419551849365},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.07128223776817322},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C46312422","wikidata":"https://www.wikidata.org/wiki/Q11024","display_name":"Communication","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/070695800","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070695800","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:832","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400452","display_name":"MIMS EPrints (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"MIMS Preprint"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.663.9416","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.663.9416","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.ma.man.ac.uk/832/01/nhom_snaking.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W141185090","https://openalex.org/W1603340857","https://openalex.org/W1866869231","https://openalex.org/W1967192224","https://openalex.org/W1979245447","https://openalex.org/W1985434612","https://openalex.org/W1988031493","https://openalex.org/W2001116478","https://openalex.org/W2015755479","https://openalex.org/W2031103701","https://openalex.org/W2033311861","https://openalex.org/W2049165066","https://openalex.org/W2049546479","https://openalex.org/W2051982903","https://openalex.org/W2082741679","https://openalex.org/W2104317722","https://openalex.org/W2112561093","https://openalex.org/W2157206636","https://openalex.org/W2168393226","https://openalex.org/W2171585207","https://openalex.org/W3106534923"],"related_works":["https://openalex.org/W2049546479","https://openalex.org/W1497977526","https://openalex.org/W3145975296","https://openalex.org/W2015099410","https://openalex.org/W2052180011","https://openalex.org/W2351007599","https://openalex.org/W2071416769","https://openalex.org/W2388443418","https://openalex.org/W1109308563","https://openalex.org/W4386724313"],"abstract_inverted_index":{"We":[0],"study":[1],"N-homoclinic":[2,33],"orbits":[3,34,44],"near":[4,38],"a":[5,9,65],"heteroclinic":[6],"cycle":[7,13],"in":[8],"reversible":[10],"system.":[11,67],"The":[12,56],"is":[14,59],"assumed":[15],"to":[16],"connect":[17],"two":[18],"equilibria":[19],"of":[20,30,53],"saddle-focus":[21],"type.":[22],"Using":[23],"Lin's":[24],"method,":[25],"we":[26],"establish":[27],"the":[28,39,51],"existence":[29],"infinitely":[31],"many":[32],"for":[35,64],"each":[36],"N":[37],"cycle.":[40],"In":[41],"particular,":[42],"these":[43],"exist":[45],"along":[46],"snaking":[47],"curves,":[48],"thus":[49],"mirroring":[50],"behavior":[52],"1-homoclinic":[54],"orbits.":[55],"general":[57],"analysis":[58],"illustrated":[60],"by":[61],"numerical":[62],"studies":[63],"Swift\u2013Hohenberg":[66]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
