{"id":"https://openalex.org/W4413155961","doi":"https://doi.org/10.1109/tac.2025.3598785","title":"Analysis of Higher Order Lotka\u2013Volterra Models: Application of $\\mathcal {S}$-Tensors and the Polynomial Complementarity Problem","display_name":"Analysis of Higher Order Lotka\u2013Volterra Models: Application of $\\mathcal {S}$-Tensors and the Polynomial Complementarity Problem","publication_year":2025,"publication_date":"2025-08-13","ids":{"openalex":"https://openalex.org/W4413155961","doi":"https://doi.org/10.1109/tac.2025.3598785"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2025.3598785","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3598785","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.rug.nl/en/publications/6ec02722-059a-47fe-9d40-350cb1bde826","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052183570","display_name":"Shaoxuan Cui","orcid":"https://orcid.org/0000-0002-2767-7244"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Shaoxuan Cui","raw_affiliation_strings":["Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, Groningen, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0002-2767-7244","affiliations":[{"raw_affiliation_string":"Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102203984","display_name":"Qi Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I143413998","display_name":"Qingdao University of Science and Technology","ror":"https://ror.org/041j8js14","country_code":"CN","type":"education","lineage":["https://openalex.org/I143413998"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qi Zhao","raw_affiliation_strings":["School of Data Science, Qingdao University of Science and Technology, Qingdao, China"],"raw_orcid":"https://orcid.org/0000-0003-1790-8309","affiliations":[{"raw_affiliation_string":"School of Data Science, Qingdao University of Science and Technology, Qingdao, China","institution_ids":["https://openalex.org/I143413998"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100693449","display_name":"Guofeng Zhang","orcid":"https://orcid.org/0000-0001-5854-5247"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Guofeng Zhang","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong","Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China"],"raw_orcid":"https://orcid.org/0000-0001-5854-5247","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029419062","display_name":"Hildeberto Jard\u00f3n-Kojakhmetov","orcid":"https://orcid.org/0000-0001-8708-7409"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Hildeberto Jard\u00f3n-Kojakhmetov","raw_affiliation_strings":["Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, Groningen, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0001-8708-7409","affiliations":[{"raw_affiliation_string":"Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021403340","display_name":"Ming Cao","orcid":"https://orcid.org/0000-0001-5472-562X"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Ming Cao","raw_affiliation_strings":["Engineering and Technology Institute Groningen, University of Groningen, Groningen, The Netherlands","Engineering and Technology Institute Groningen, University of Groningen, Groningen, AG, Netherlands"],"raw_orcid":"https://orcid.org/0000-0001-5472-562X","affiliations":[{"raw_affiliation_string":"Engineering and Technology Institute Groningen, University of Groningen, Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]},{"raw_affiliation_string":"Engineering and Technology Institute Groningen, University of Groningen, Groningen, AG, Netherlands","institution_ids":["https://openalex.org/I169381384"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4253,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.79657825,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"71","issue":"2","first_page":"737","last_page":"752"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10842","display_name":"Railway Engineering and Dynamics","score":0.76419997215271,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10842","display_name":"Railway Engineering and Dynamics","score":0.76419997215271,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.7184973955154419},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.61040198802948},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.588417112827301},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5066784024238586},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.484110951423645},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4110889434814453},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3716159760951996},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28296899795532227},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.09806832671165466}],"concepts":[{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.7184973955154419},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.61040198802948},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.588417112827301},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5066784024238586},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.484110951423645},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4110889434814453},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3716159760951996},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28296899795532227},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.09806832671165466},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tac.2025.3598785","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3598785","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:pure.rug.nl:openaire_cris_publications/6ec02722-059a-47fe-9d40-350cb1bde826","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/6ec02722-059a-47fe-9d40-350cb1bde826","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cui, S, Zhao, Q, Zhang, G, Jard\u00f3n-Kojakhmetov, H & Cao, M 2026, 'Analysis of higher-order Lotka-Volterra models : Application of S-tensors and the polynomial complementarity problem', IEEE Transactions on Automatic Control, vol. 71, no. 2, pp. 737-752. https://doi.org/10.1109/TAC.2025.3598785","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.rug.nl:openaire/6ec02722-059a-47fe-9d40-350cb1bde826","is_oa":true,"landing_page_url":"https://hdl.handle.net/11370/6ec02722-059a-47fe-9d40-350cb1bde826","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cui, S, Zhao, Q, Zhang, G, Jard\u00f3n-Kojakhmetov, H & Cao, M 2026, 'Analysis of higher-order Lotka-Volterra models : Application of S-tensors and the polynomial complementarity problem', IEEE Transactions on Automatic Control, vol. 71, no. 2, pp. 737-752. https://doi.org/10.1109/TAC.2025.3598785","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:pure.rug.nl:openaire_cris_publications/6ec02722-059a-47fe-9d40-350cb1bde826","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/6ec02722-059a-47fe-9d40-350cb1bde826","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cui, S, Zhao, Q, Zhang, G, Jard\u00f3n-Kojakhmetov, H & Cao, M 2026, 'Analysis of higher-order Lotka-Volterra models : Application of S-tensors and the polynomial complementarity problem', IEEE Transactions on Automatic Control, vol. 71, no. 2, pp. 737-752. https://doi.org/10.1109/TAC.2025.3598785","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1197550583","display_name":null,"funder_award_id":"62173288","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8851761500","display_name":null,"funder_award_id":"25-1-1-121-zyyd-jch","funder_id":"https://openalex.org/F4320328636","funder_display_name":"Natural Science Foundation of Qingdao"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320328636","display_name":"Natural Science Foundation of Qingdao","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1736530648","https://openalex.org/W1977738976","https://openalex.org/W2002687251","https://openalex.org/W2010989175","https://openalex.org/W2012593053","https://openalex.org/W2033489353","https://openalex.org/W2038227189","https://openalex.org/W2047681048","https://openalex.org/W2061011338","https://openalex.org/W2063011550","https://openalex.org/W2069850422","https://openalex.org/W2081363984","https://openalex.org/W2085728653","https://openalex.org/W2090208105","https://openalex.org/W2095057493","https://openalex.org/W2112660220","https://openalex.org/W2120001551","https://openalex.org/W2136020357","https://openalex.org/W2222111999","https://openalex.org/W2588670633","https://openalex.org/W2911484707","https://openalex.org/W2946480664","https://openalex.org/W2953006003","https://openalex.org/W2966845367","https://openalex.org/W3085929068","https://openalex.org/W3134218762","https://openalex.org/W3158396846","https://openalex.org/W3174824658","https://openalex.org/W3202435984","https://openalex.org/W3213154861","https://openalex.org/W4230451458","https://openalex.org/W4293334944","https://openalex.org/W4306642903","https://openalex.org/W4382935953","https://openalex.org/W4409633836"],"related_works":["https://openalex.org/W1527041535","https://openalex.org/W2521519254","https://openalex.org/W3139833644","https://openalex.org/W3123110765","https://openalex.org/W4383553409","https://openalex.org/W2104948296","https://openalex.org/W1735800226","https://openalex.org/W4285172739","https://openalex.org/W3123208392","https://openalex.org/W2110047879"],"abstract_inverted_index":{"It":[0],"is":[1,12],"known":[2],"that":[3],"the":[4,20,25,51,92,99,105,113,122,128,144,150],"effect":[5,53],"of":[6,54,81,94,107,127,139,152],"species'":[7],"density":[8],"on":[9,57],"its":[10],"growth":[11],"non-additive":[13],"in":[14,149],"real":[15],"ecological":[16],"systems.":[17],"This":[18],"challenges":[19],"conventional":[21],"Lotka-Volterra":[22,74,146],"model,":[23,147],"where":[24],"interactions":[26],"are":[27,33,45,166],"always":[28],"pairwise":[29],"and":[30,110,125,159],"their":[31],"effects":[32],"additive.":[34],"To":[35],"address":[36],"this":[37,67],"challenge,":[38],"we":[39,69,117],"introduce":[40],"HOIs":[41],"(Higher-Order":[42],"Interactions)":[43],"which":[44],"able":[46],"to":[47,62,168],"capture,":[48],"for":[49,85,143],"example,":[50],"indirect":[52],"one":[55,60],"species":[56],"a":[58,64,71,82,86],"second":[59],"correlating":[61],"yet":[63],"third.":[65],"Towards":[66],"end,":[68],"study":[70],"general":[72],"higher-order":[73],"model.":[75],"We":[76],"provide":[77,118],"an":[78],"existence":[79],"result":[80],"positive":[83],"equilibrium":[84],"nonhomogeneous":[87],"polynomial":[88,114],"equation":[89],"system":[90],"with":[91],"help":[93],"S-tensors.":[95],"Afterward,":[96],"by":[97],"utilizing":[98],"latter":[100],"result,":[101],"as":[102,104,136],"well":[103],"theory":[106],"monotone":[108],"systems":[109],"results":[111,120,132],"from":[112],"complementarity":[115],"problem,":[116],"comprehensive":[119],"regarding":[121],"existence,":[123],"uniqueness,":[124],"stability":[126],"corresponding":[129],"equilibrium.":[130],"These":[131],"can":[133],"be":[134],"regarded":[135],"natural":[137],"extensions":[138],"many":[140],"similar":[141],"ones":[142],"classical":[145],"especially":[148],"case":[151],"full":[153],"cooperation,":[154],"competition":[155],"among":[156],"two":[157],"factions,":[158],"pure":[160],"competition.":[161],"Finally,":[162],"illustrative":[163],"numerical":[164],"examples":[165],"provided":[167],"highlight":[169],"our":[170],"contributions.":[171]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
