{"id":"https://openalex.org/W2966299158","doi":"https://doi.org/10.1142/s0218127419501050","title":"Global Invariant Manifolds of Dynamical Systems with the Compatible Cell Mapping Method","display_name":"Global Invariant Manifolds of Dynamical Systems with the Compatible Cell Mapping Method","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2966299158","doi":"https://doi.org/10.1142/s0218127419501050","mag":"2966299158"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127419501050","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419501050","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061543625","display_name":"Xiaole Yue","orcid":"https://orcid.org/0000-0003-2983-5821"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao-Le Yue","raw_affiliation_strings":["Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an 710072, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an 710072, P. R. China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062310230","display_name":"Yong Xu","orcid":"https://orcid.org/0000-0002-8407-4650"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong Xu","raw_affiliation_strings":["Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an 710072, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an 710072, P. R. China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102009272","display_name":"Wei Xu","orcid":"https://orcid.org/0000-0002-7822-0340"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Xu","raw_affiliation_strings":["Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an 710072, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an 710072, P. R. China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017350937","display_name":"Jian\u2010Qiao Sun","orcid":"https://orcid.org/0000-0002-5441-7982"},"institutions":[{"id":"https://openalex.org/I156087764","display_name":"University of California, Merced","ror":"https://ror.org/00d9ah105","country_code":"US","type":"education","lineage":["https://openalex.org/I156087764"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jian-Qiao Sun","raw_affiliation_strings":["Department of Mechanical Engineering, School of Engineering, University of California, Merced, CA 95343, USA"],"raw_orcid":"https://orcid.org/0000-0002-5441-7982","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, School of Engineering, University of California, Merced, CA 95343, USA","institution_ids":["https://openalex.org/I156087764"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8595,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.87000309,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"29","issue":"08","first_page":"1950105","last_page":"1950105"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9977999925613403,"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":0.9977999925613403,"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":0.9857000112533569,"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/T10244","display_name":"Chaos control and synchronization","score":0.9850000143051147,"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/digraph","display_name":"Digraph","score":0.7027466297149658},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6664438247680664},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.6088168621063232},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6062218546867371},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5962329506874084},{"id":"https://openalex.org/keywords/sort","display_name":"sort","score":0.5299758911132812},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4847840666770935},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4449802041053772},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.42357420921325684},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4015507698059082},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39785343408584595},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3560079336166382},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34285855293273926},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2801464796066284},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.27509987354278564},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20015448331832886},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.13407716155052185},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10459282994270325},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07443320751190186}],"concepts":[{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.7027466297149658},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6664438247680664},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.6088168621063232},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6062218546867371},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5962329506874084},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.5299758911132812},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4847840666770935},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4449802041053772},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.42357420921325684},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4015507698059082},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39785343408584595},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3560079336166382},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34285855293273926},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2801464796066284},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27509987354278564},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20015448331832886},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.13407716155052185},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10459282994270325},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07443320751190186},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127419501050","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419501050","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2161524796","display_name":null,"funder_award_id":"11332008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7363664854","display_name":null,"funder_award_id":"11672230","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G77775792","display_name":null,"funder_award_id":"11572215","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W49685413","https://openalex.org/W97642424","https://openalex.org/W154986292","https://openalex.org/W1485705287","https://openalex.org/W1575974143","https://openalex.org/W1770420856","https://openalex.org/W1933216107","https://openalex.org/W1968639412","https://openalex.org/W1972010123","https://openalex.org/W1990710413","https://openalex.org/W2000473820","https://openalex.org/W2001659478","https://openalex.org/W2002942449","https://openalex.org/W2012068782","https://openalex.org/W2024743713","https://openalex.org/W2025475113","https://openalex.org/W2028044614","https://openalex.org/W2043282743","https://openalex.org/W2044371775","https://openalex.org/W2045565588","https://openalex.org/W2047878675","https://openalex.org/W2048101935","https://openalex.org/W2049739431","https://openalex.org/W2051266746","https://openalex.org/W2063467803","https://openalex.org/W2065389195","https://openalex.org/W2071248198","https://openalex.org/W2077011938","https://openalex.org/W2089876099","https://openalex.org/W2089897697","https://openalex.org/W2091298827","https://openalex.org/W2093130989","https://openalex.org/W2101021792","https://openalex.org/W2164761951","https://openalex.org/W2171972705","https://openalex.org/W2213248130","https://openalex.org/W2403208851","https://openalex.org/W2532470853","https://openalex.org/W2794394439","https://openalex.org/W2801813398","https://openalex.org/W4230906466","https://openalex.org/W4244438451"],"related_works":["https://openalex.org/W4236459141","https://openalex.org/W4205304778","https://openalex.org/W2020252434","https://openalex.org/W73248859","https://openalex.org/W2584253892","https://openalex.org/W2350324449","https://openalex.org/W119381072","https://openalex.org/W2034033896","https://openalex.org/W2094891943","https://openalex.org/W4240399920"],"abstract_inverted_index":{"An":[0],"iterative":[1,139],"compatible":[2,74],"cell":[3,42,60,134],"mapping":[4,43,61],"(CCM)":[5],"method":[6,45,63,111,144],"with":[7,25,122,166],"the":[8,18,51,58,76,79,85,95,115,123,142,156,159,162,180,184,190,209],"digraph":[9,109,152],"theory":[10],"is":[11,46,81,91,112,145,171],"presented":[12],"in":[13,75,173,179],"this":[14,106,128],"paper":[15],"to":[16,49,93,204,208],"compute":[17],"global":[19,99,185],"invariant":[20,186],"manifolds":[21,103],"of":[22,84,98,141,158],"dynamical":[23],"systems":[24],"high":[26,29],"precision":[27],"and":[28,34,71,101,151,192],"efficiency.":[30],"The":[31,40,54,69,87,108,196],"accurate":[32],"attractors":[33,191],"saddles":[35,170,193],"can":[36,199],"be":[37,120,200],"simultaneously":[38],"obtained.":[39],"simple":[41],"(SCM)":[44],"first":[47],"used":[48,113],"obtain":[50],"periodic":[52,117,167],"solutions.":[53],"results":[55],"obtained":[56,121],"by":[57,147,202],"generalized":[59],"(GCM)":[62],"are":[64,73,194],"treated":[65],"as":[66,131],"a":[67,82,132],"database.":[68,107],"SCM":[70,80,124],"GCM":[72,110,211],"sense":[77],"that":[78],"subset":[83],"GCM.":[86],"depth-first":[88],"search":[89,150],"algorithm":[90],"utilized":[92],"find":[94],"coarse":[96,129],"coverings":[97],"stable":[100],"unstable":[102],"based":[104],"on":[105],"if":[114],"saddle-like":[116],"solutions":[118],"cannot":[119],"method.":[125,212],"By":[126],"taking":[127],"covering":[130],"new":[133],"state":[135],"space,":[136],"an":[137],"efficient":[138],"procedure":[140],"CCM":[143],"proposed":[146,160],"combining":[148],"sort,":[149],"algorithms.":[153],"To":[154],"demonstrate":[155],"effectiveness":[157],"method,":[161],"classical":[163],"H\u00e9non":[164],"map":[165],"or":[168],"chaotic":[169],"studied":[172],"far":[174],"more":[175],"depth":[176],"than":[177],"reported":[178],"literature.":[181],"Not":[182],"only":[183],"manifolds,":[187],"but":[188],"also":[189],"computed.":[195],"computational":[197],"efficiency":[198],"improved":[201],"up":[203],"200":[205],"times":[206],"compared":[207],"traditional":[210]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
