{"id":"https://openalex.org/W4377091935","doi":"https://doi.org/10.3390/axioms12050501","title":"Dynamics in an n-Species Lotka\u2013Volterra Cooperative System with Delays","display_name":"Dynamics in an n-Species Lotka\u2013Volterra Cooperative System with Delays","publication_year":2023,"publication_date":"2023-05-19","ids":{"openalex":"https://openalex.org/W4377091935","doi":"https://doi.org/10.3390/axioms12050501"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12050501","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12050501","pdf_url":"https://www.mdpi.com/2075-1680/12/5/501/pdf?version=1684822982","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/5/501/pdf?version=1684822982","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101756973","display_name":"Jiang Zhao","orcid":"https://orcid.org/0000-0002-9180-9520"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhao Jiang","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China","The Key Laboratory of Applied Mathematics of Xinjiang, Uygur Autonomous Region, Xinjiang University, Urumqi 830017, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China","institution_ids":["https://openalex.org/I96908189"]},{"raw_affiliation_string":"The Key Laboratory of Applied Mathematics of Xinjiang, Uygur Autonomous Region, Xinjiang University, Urumqi 830017, China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063538831","display_name":"Azhar Halik","orcid":null},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Azhar Halik","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051287601","display_name":"Ahmadjan Muhammadhaji","orcid":"https://orcid.org/0000-0002-2596-9489"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ahmadjan Muhammadhaji","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China","The Key Laboratory of Applied Mathematics of Xinjiang, Uygur Autonomous Region, Xinjiang University, Urumqi 830017, China"],"raw_orcid":"https://orcid.org/0000-0002-2596-9489","affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China","institution_ids":["https://openalex.org/I96908189"]},{"raw_affiliation_string":"The Key Laboratory of Applied Mathematics of Xinjiang, Uygur Autonomous Region, Xinjiang University, Urumqi 830017, China","institution_ids":["https://openalex.org/I96908189"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051287601"],"corresponding_institution_ids":["https://openalex.org/I96908189"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.9541,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.74312286,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"12","issue":"5","first_page":"501","last_page":"501"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9869999885559082,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T13377","display_name":"Ecosystem dynamics and resilience","score":0.9667999744415283,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.8447537422180176},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7285335063934326},{"id":"https://openalex.org/keywords/coincidence","display_name":"Coincidence","score":0.5635053515434265},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5382580161094666},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5155422687530518},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5084397196769714},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4985055923461914},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.45822107791900635},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.201680988073349},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1409931182861328},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.06494179368019104},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.060466766357421875},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0524466335773468},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.04475200176239014}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.8447537422180176},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7285335063934326},{"id":"https://openalex.org/C2779832538","wikidata":"https://www.wikidata.org/wiki/Q2308809","display_name":"Coincidence","level":3,"score":0.5635053515434265},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5382580161094666},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5155422687530518},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5084397196769714},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4985055923461914},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.45822107791900635},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.201680988073349},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1409931182861328},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.06494179368019104},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.060466766357421875},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0524466335773468},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.04475200176239014},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","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},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C204787440","wikidata":"https://www.wikidata.org/wiki/Q188504","display_name":"Alternative medicine","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12050501","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12050501","pdf_url":"https://www.mdpi.com/2075-1680/12/5/501/pdf?version=1684822982","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/5/501/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12050501","pdf_url":"https://dx.doi.org/10.3390/axioms12050501","source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 12; Issue 5; Pages: 501","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:a3dc175eb4924803b0e44394b09c6fd0","is_oa":true,"landing_page_url":"https://doaj.org/article/a3dc175eb4924803b0e44394b09c6fd0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 5, p 501 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms12050501","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12050501","pdf_url":"https://www.mdpi.com/2075-1680/12/5/501/pdf?version=1684822982","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320328898","display_name":"Natural Science Foundation of Xinjiang","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4377091935.pdf","grobid_xml":"https://content.openalex.org/works/W4377091935.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1607588772","https://openalex.org/W1974900728","https://openalex.org/W1988939360","https://openalex.org/W2015795316","https://openalex.org/W2019336455","https://openalex.org/W2026084291","https://openalex.org/W2040941239","https://openalex.org/W2059633261","https://openalex.org/W2064923068","https://openalex.org/W2092582457","https://openalex.org/W2154105245","https://openalex.org/W2158720758","https://openalex.org/W2317771247","https://openalex.org/W2326877587","https://openalex.org/W2734511519","https://openalex.org/W2805425560","https://openalex.org/W2894651388","https://openalex.org/W2995603090","https://openalex.org/W3001105918","https://openalex.org/W4308332761","https://openalex.org/W4313408589","https://openalex.org/W4318197690","https://openalex.org/W6644005551"],"related_works":["https://openalex.org/W3029319512","https://openalex.org/W3033220593","https://openalex.org/W2138100553","https://openalex.org/W2007743448","https://openalex.org/W1990560562","https://openalex.org/W2070733898","https://openalex.org/W4389454697","https://openalex.org/W1911643999","https://openalex.org/W3022014457","https://openalex.org/W2798159474"],"abstract_inverted_index":{"We":[0,15],"studied":[1],"a":[2],"class":[3],"of":[4,23,33,47,61,80,99],"generalized":[5],"n-species":[6],"non-autonomous":[7],"cooperative":[8],"Lotka\u2013Volterra":[9],"(L-V)":[10],"systems":[11],"with":[12],"time":[13],"delays.":[14],"obtained":[16,28,65],"new":[17],"criteria":[18],"on":[19],"the":[20,24,29,34,37,45,54,62,81,95],"dynamic":[21],"properties":[22],"systems.":[25],"First,":[26],"we":[27,88],"boundedness":[30],"and":[31,41,71,77,97],"permanence":[32],"system":[35,63],"using":[36,53],"inequality":[38],"analysis":[39],"technique":[40],"comparison":[42],"method.":[43],"Then,":[44],"existence":[46,76],"positive":[48],"periodic":[49,82],"solutions":[50,83],"was":[51,64],"investigated":[52],"coincidence":[55],"degree":[56],"theory.":[57],"The":[58,75],"global":[59,78],"attractivity":[60,79],"by":[66],"constructing":[67],"suitable":[68],"Lyapunov":[69],"functionals":[70],"utilizing":[72],"Barbalat\u2019s":[73],"lemma.":[74],"were":[84],"also":[85],"obtained.":[86],"Finally,":[87],"conducted":[89],"two":[90],"numerical":[91],"simulations":[92],"to":[93],"validate":[94],"feasibility":[96],"practicability":[98],"our":[100],"results.":[101]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2023-05-20T00:00:00"}
