{"id":"https://openalex.org/W4412667282","doi":"https://doi.org/10.1142/s0218127425501494","title":"Multiple Periodic Orbits of Odd-Order Delay Differential Systems","display_name":"Multiple Periodic Orbits of Odd-Order Delay Differential Systems","publication_year":2025,"publication_date":"2025-07-25","ids":{"openalex":"https://openalex.org/W4412667282","doi":"https://doi.org/10.1142/s0218127425501494"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127425501494","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425501494","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/A5111761276","display_name":"Lin Li","orcid":null},"institutions":[{"id":"https://openalex.org/I179026463","display_name":"Beijing Technology and Business University","ror":"https://ror.org/013e0zm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I179026463"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lin Li","raw_affiliation_strings":["School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, P.\u00a0R.\u00a0China"],"raw_orcid":"https://orcid.org/0009-0009-0378-3948","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I179026463"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082768575","display_name":"Bo Sun","orcid":"https://orcid.org/0000-0002-6795-818X"},"institutions":[{"id":"https://openalex.org/I137867983","display_name":"Central University of Finance and Economics","ror":"https://ror.org/008e3hf02","country_code":"CN","type":"education","lineage":["https://openalex.org/I137867983"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Sun","raw_affiliation_strings":["School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, P.\u00a0R.\u00a0China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I137867983"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102049257","display_name":"Weigao Ge","orcid":null},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weigao Ge","raw_affiliation_strings":["School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.\u00a0R.\u00a0China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I125839683"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5111761276"],"corresponding_institution_ids":["https://openalex.org/I179026463"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12889155,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":"12","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9132999777793884,"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":0.9132999777793884,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9045000076293945,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.609696626663208},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5907907485961914},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5282593965530396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5177011489868164},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.4921075701713562},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4578515291213989},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3765944838523865},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34321361780166626},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3320334851741791},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.29233384132385254},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23670625686645508},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.11378708481788635},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.09817400574684143}],"concepts":[{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.609696626663208},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5907907485961914},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5282593965530396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5177011489868164},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.4921075701713562},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4578515291213989},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3765944838523865},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34321361780166626},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3320334851741791},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29233384132385254},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23670625686645508},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.11378708481788635},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.09817400574684143},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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:10.1142/s0218127425501494","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425501494","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1575983931","https://openalex.org/W1969953268","https://openalex.org/W1976842194","https://openalex.org/W1998401374","https://openalex.org/W2007709253","https://openalex.org/W2016688958","https://openalex.org/W2029216342","https://openalex.org/W2043097947","https://openalex.org/W2050514626","https://openalex.org/W2066996899","https://openalex.org/W2071682920","https://openalex.org/W2085139909","https://openalex.org/W2104048931","https://openalex.org/W2360452163","https://openalex.org/W2524411354","https://openalex.org/W2914059566","https://openalex.org/W2996822832","https://openalex.org/W3015610213","https://openalex.org/W3091777858","https://openalex.org/W4230357017"],"related_works":["https://openalex.org/W1261320338","https://openalex.org/W2056281781","https://openalex.org/W2924035449","https://openalex.org/W2086307616","https://openalex.org/W2942981489","https://openalex.org/W4243954292","https://openalex.org/W2903509708","https://openalex.org/W2977631248","https://openalex.org/W2753150188","https://openalex.org/W2389579716"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,55],"study":[4],"the":[5,28,46,64],"periodic":[6,67],"orbits":[7],"in":[8,31,43],"a":[9,37,57],"type":[10],"of":[11,66],"odd-order":[12],"differential":[13,47],"delay":[14],"systems":[15],"with":[16],"[Formula:":[17],"see":[18],"text]":[19],"lags":[20],"which":[21],"has":[22],"not":[23],"been":[24],"studied":[25],"due":[26],"to":[27],"great":[29],"difficulty":[30],"constructing":[32],"differentiable":[33],"functionals.":[34],"We":[35],"develop":[36],"method":[38,61],"for":[39,62],"functional":[40],"construction,":[41],"and":[42],"particular,":[44],"when":[45],"system":[48],"can":[49],"be":[50],"decomposed":[51],"into":[52],"several":[53],"systems,":[54],"provide":[56],"more":[58],"accurate":[59],"calculation":[60],"estimating":[63],"number":[65],"orbits.":[68]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
