{"id":"https://openalex.org/W2329631904","doi":"https://doi.org/10.1142/s0218127416500498","title":"Traveling Waves Connecting Equilibrium and Periodic Orbit for a Delayed Population Model on a Two-Dimensional Spatial Lattice","display_name":"Traveling Waves Connecting Equilibrium and Periodic Orbit for a Delayed Population Model on a Two-Dimensional Spatial Lattice","publication_year":2016,"publication_date":"2016-03-01","ids":{"openalex":"https://openalex.org/W2329631904","doi":"https://doi.org/10.1142/s0218127416500498","mag":"2329631904"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416500498","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500498","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/A5103640541","display_name":"Cui-Ping Cheng","orcid":null},"institutions":[{"id":"https://openalex.org/I67001856","display_name":"Shanghai Institute of Technology","ror":"https://ror.org/00fjzqj15","country_code":"CN","type":"education","lineage":["https://openalex.org/I67001856"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Cui-Ping Cheng","raw_affiliation_strings":["School of Science, Shanghai Institute of Technology, Shanghai 201418, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Shanghai Institute of Technology, Shanghai 201418, P. R. China","institution_ids":["https://openalex.org/I67001856"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078633614","display_name":"Wan\u2010Tong Li","orcid":"https://orcid.org/0000-0002-1653-3691"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wan-Tong Li","raw_affiliation_strings":["School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P. R. China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100429164","display_name":"Zhi\u2010Cheng Wang","orcid":"https://orcid.org/0000-0001-6998-937X"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi-Cheng Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P. R. China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028331125","display_name":"Shenzhou Zheng","orcid":"https://orcid.org/0000-0002-7909-0517"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shenzhou Zheng","raw_affiliation_strings":["Department of Mathematics, Beijing Jiaotong University, Beijing 100044, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Beijing Jiaotong University, Beijing 100044, P. R. China","institution_ids":["https://openalex.org/I21193070"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103640541"],"corresponding_institution_ids":["https://openalex.org/I67001856"],"apc_list":null,"apc_paid":null,"fwci":0.9121,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.80561601,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"26","issue":"03","first_page":"1650049","last_page":"1650049"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9873999953269958,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7200519442558289},{"id":"https://openalex.org/keywords/heteroclinic-orbit","display_name":"Heteroclinic orbit","score":0.6626954078674316},{"id":"https://openalex.org/keywords/population-model","display_name":"Population model","score":0.6265038251876831},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5916783213615417},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.5828843116760254},{"id":"https://openalex.org/keywords/implicit-function-theorem","display_name":"Implicit function theorem","score":0.5446072220802307},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5167297720909119},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5110498666763306},{"id":"https://openalex.org/keywords/traveling-wave","display_name":"Traveling wave","score":0.4982914924621582},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.479850709438324},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.43744492530822754},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.4147844910621643},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.3963015675544739},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20100882649421692},{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.1799945831298828},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.16314664483070374},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12518930435180664}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7200519442558289},{"id":"https://openalex.org/C184481792","wikidata":"https://www.wikidata.org/wiki/Q1992087","display_name":"Heteroclinic orbit","level":5,"score":0.6626954078674316},{"id":"https://openalex.org/C52079815","wikidata":"https://www.wikidata.org/wiki/Q7229808","display_name":"Population model","level":3,"score":0.6265038251876831},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5916783213615417},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.5828843116760254},{"id":"https://openalex.org/C138578839","wikidata":"https://www.wikidata.org/wiki/Q848375","display_name":"Implicit function theorem","level":2,"score":0.5446072220802307},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5167297720909119},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5110498666763306},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.4982914924621582},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.479850709438324},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.43744492530822754},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.4147844910621643},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.3963015675544739},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20100882649421692},{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.1799945831298828},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.16314664483070374},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12518930435180664},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218127416500498","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500498","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:ir.lzu.edu.cn/:262010/180796","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/180796","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","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":"Article"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/400446","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/400446","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","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":"Journal article (JA)"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1483675707","https://openalex.org/W1491610348","https://openalex.org/W1589242138","https://openalex.org/W1966918929","https://openalex.org/W1968267631","https://openalex.org/W1974007280","https://openalex.org/W1974439340","https://openalex.org/W1977183861","https://openalex.org/W1978725093","https://openalex.org/W1997602286","https://openalex.org/W1998734287","https://openalex.org/W2000937327","https://openalex.org/W2015899817","https://openalex.org/W2016767879","https://openalex.org/W2018736354","https://openalex.org/W2027325698","https://openalex.org/W2028915135","https://openalex.org/W2029607875","https://openalex.org/W2030109220","https://openalex.org/W2030374035","https://openalex.org/W2034823941","https://openalex.org/W2036391010","https://openalex.org/W2046960180","https://openalex.org/W2056934355","https://openalex.org/W2062719082","https://openalex.org/W2078321203","https://openalex.org/W2078927495","https://openalex.org/W2079871064","https://openalex.org/W2090287158","https://openalex.org/W2101495277","https://openalex.org/W2105206465","https://openalex.org/W2113868787","https://openalex.org/W2146755474","https://openalex.org/W2156641145","https://openalex.org/W2164949167","https://openalex.org/W2168257429","https://openalex.org/W2170185911","https://openalex.org/W2182970790","https://openalex.org/W2507047444"],"related_works":["https://openalex.org/W1497977526","https://openalex.org/W2040151997","https://openalex.org/W2026653107","https://openalex.org/W2996959914","https://openalex.org/W2383053365","https://openalex.org/W2366154005","https://openalex.org/W2055410928","https://openalex.org/W2131818693","https://openalex.org/W1986164386","https://openalex.org/W2329631904"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,93],"concerned":[3],"with":[4,23],"the":[5,32,35,54,69,97],"existence":[6,87],"of":[7,88],"fast":[8],"traveling":[9,89],"waves":[10],"connecting":[11,41],"an":[12,42,60],"equilibrium":[13,43],"and":[14,45,67,100],"a":[15,19,27,46,64,77,82],"periodic":[16,47],"orbit":[17],"in":[18,63],"delayed":[20],"population":[21],"model":[22],"stage":[24],"structure":[25],"on":[26],"two-dimensional":[28],"spatial":[29],"lattice,":[30],"under":[31],"assumption":[33],"that":[34],"corresponding":[36,70],"ODEs":[37],"have":[38],"heteroclinic":[39],"orbits":[40],"point":[44],"solution.":[48],"In":[49],"this":[50],"work,":[51],"we":[52],"rewrite":[53],"mixed":[55],"functional":[56],"differential":[57],"equation":[58,62],"as":[59],"integral":[61],"Banach":[65],"space":[66],"analyze":[68],"linear":[71],"operator.":[72],"Our":[73],"approach":[74],"eventually":[75],"reduces":[76],"singular":[78],"perturbation":[79,84],"problem":[80],"to":[81],"regular":[83],"problem.":[85],"The":[86],"wave":[90],"solution":[91],"therefore":[92],"obtained":[94],"by":[95],"using":[96],"Liapunov\u2013Schmidt":[98],"method":[99],"implicit":[101],"function":[102],"theorem.":[103]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}