{"id":"https://openalex.org/W2903051627","doi":"https://doi.org/10.1186/s13662-018-1891-5","title":"Permanence and extinction of a high-dimensional stochastic resource competition model with noise","display_name":"Permanence and extinction of a high-dimensional stochastic resource competition model with noise","publication_year":2018,"publication_date":"2018-11-28","ids":{"openalex":"https://openalex.org/W2903051627","doi":"https://doi.org/10.1186/s13662-018-1891-5","mag":"2903051627"},"language":"en","primary_location":{"id":"doi:10.1186/s13662-018-1891-5","doi":"https://doi.org/10.1186/s13662-018-1891-5","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13662-018-1891-5","pdf_url":"https://advancesindifferenceequations.springeropen.com/track/pdf/10.1186/s13662-018-1891-5","source":{"id":"https://openalex.org/S169017477","display_name":"Advances in Difference Equations","issn_l":"1687-1839","issn":["1687-1839","1687-1847"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Difference Equations","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://advancesindifferenceequations.springeropen.com/track/pdf/10.1186/s13662-018-1891-5","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100336032","display_name":"Li Wang","orcid":"https://orcid.org/0009-0001-1822-5887","observed_orcids":["https://orcid.org/0009-0001-1822-5887"]},"institutions":[{"id":"https://openalex.org/I21642278","display_name":"Ningxia University","ror":"https://ror.org/04j7b2v61","country_code":"CN","type":"education","lineage":["https://openalex.org/I21642278"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Ningxia University, Ningxia, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Ningxia University, Ningxia, China","institution_ids":["https://openalex.org/I21642278"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100626803","display_name":"Xiaoqiang Wang","orcid":"https://orcid.org/0000-0003-0960-521X","observed_orcids":["https://orcid.org/0000-0003-0960-521X","https://orcid.org/0000-0003-1825-0895"]},"institutions":[{"id":"https://openalex.org/I103163165","display_name":"Florida State University","ror":"https://ror.org/05g3dte14","country_code":"US","type":"education","lineage":["https://openalex.org/I103163165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaoqiang Wang","raw_affiliation_strings":["Department of Scientific Computing, Florida State University, Tallahassee, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Scientific Computing, Florida State University, Tallahassee, USA","institution_ids":["https://openalex.org/I103163165"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060957183","display_name":"Qimin Zhang","orcid":"https://orcid.org/0000-0002-6099-2799","observed_orcids":["https://orcid.org/0000-0002-6099-2799","https://orcid.org/0000-0002-5851-0957"]},"institutions":[{"id":"https://openalex.org/I21642278","display_name":"Ningxia University","ror":"https://ror.org/04j7b2v61","country_code":"CN","type":"education","lineage":["https://openalex.org/I21642278"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qimin Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Ningxia University, Ningxia, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Ningxia University, Ningxia, China","institution_ids":["https://openalex.org/I21642278"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5060957183"],"corresponding_institution_ids":["https://openalex.org/I21642278"],"apc_list":{"value":1790,"currency":"USD","value_usd":1790},"apc_paid":{"value":1790,"currency":"USD","value_usd":1790},"fwci":0.4434,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.69089993,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":94},"biblio":{"volume":"2018","issue":"1","first_page":null,"last_page":null},"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":0.9990000128746033,"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":0.9990000128746033,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.00019999999494757503,"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/stochastic-population-dynamics","display_name":"stochastic population dynamics","score":0.6299999952316284},{"id":"https://openalex.org/keywords/white-noise","display_name":"white noise","score":0.8529999852180481},{"id":"https://openalex.org/keywords/permanence","display_name":"permanence","score":0.9649999737739563},{"id":"https://openalex.org/keywords/extinction","display_name":"extinction","score":0.9990000128746033},{"id":"https://openalex.org/keywords/high-dimensional-systems","display_name":"high-dimensional systems","score":0.7289999723434448},{"id":"https://openalex.org/keywords/lyapunov-functional","display_name":"Lyapunov functional","score":0.9660000205039978},{"id":"https://openalex.org/keywords/trajectory-estimation","display_name":"trajectory estimation","score":0.7870000004768372},{"id":"https://openalex.org/keywords/noise-intensity","display_name":"noise intensity","score":0.8220000267028809}],"concepts":[{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.767023503780365},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7504007816314697},{"id":"https://openalex.org/C2779396167","wikidata":"https://www.wikidata.org/wiki/Q5156040","display_name":"Comparison theorem","level":2,"score":0.7176308631896973},{"id":"https://openalex.org/C101991246","wikidata":"https://www.wikidata.org/wiki/Q5422078","display_name":"Extinction (optical mineralogy)","level":2,"score":0.6630457639694214},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5748336911201477},{"id":"https://openalex.org/C91306197","wikidata":"https://www.wikidata.org/wiki/Q45767","display_name":"Competition (biology)","level":2,"score":0.5354787111282349},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4792037904262543},{"id":"https://openalex.org/C86781634","wikidata":"https://www.wikidata.org/wiki/Q2478325","display_name":"Environmental noise","level":3,"score":0.4674319624900818},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.44485679268836975},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31566429138183594},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20594778656959534},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1522364318370819},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15023580193519592},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0827602744102478},{"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/C203718221","wikidata":"https://www.wikidata.org/wiki/Q491713","display_name":"Sound (geography)","level":2,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","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/C114793014","wikidata":"https://www.wikidata.org/wiki/Q52109","display_name":"Geomorphology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1186/s13662-018-1891-5","doi":"https://doi.org/10.1186/s13662-018-1891-5","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13662-018-1891-5","pdf_url":"https://advancesindifferenceequations.springeropen.com/track/pdf/10.1186/s13662-018-1891-5","source":{"id":"https://openalex.org/S169017477","display_name":"Advances in Difference Equations","issn_l":"1687-1839","issn":["1687-1839","1687-1847"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Difference Equations","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:10612a54ddf149e193f48745bd5f71d8","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/10612a54ddf149e193f48745bd5f71d8","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,"listed_in":[],"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":"Advances in Difference Equations, Vol 2018, Iss 1, Pp 1-18 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1186/s13662-018-1891-5","doi":"https://doi.org/10.1186/s13662-018-1891-5","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13662-018-1891-5","pdf_url":"https://advancesindifferenceequations.springeropen.com/track/pdf/10.1186/s13662-018-1891-5","source":{"id":"https://openalex.org/S169017477","display_name":"Advances in Difference Equations","issn_l":"1687-1839","issn":["1687-1839","1687-1847"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Difference Equations","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.4300000071525574,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"study_designs":[],"awards":[{"id":"https://openalex.org/G6629749551","display_name":"\u57fa\u4e8e\u566a\u58f0\u5f71\u54cd\u7684\u751f\u7269\u4fee\u590d\u7cfb\u7edf\u6e10\u8fd1\u884c\u4e3a\u53ca\u6570\u503c\u8ba1\u7b97\u65b9\u6cd5\u7814\u7a76","funder_award_id":"11661064","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2903051627.pdf","grobid_xml":"https://content.openalex.org/works/W2903051627.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1488595547","https://openalex.org/W1937257198","https://openalex.org/W1966369958","https://openalex.org/W1967275195","https://openalex.org/W1973119612","https://openalex.org/W1974190671","https://openalex.org/W1980191241","https://openalex.org/W1988025776","https://openalex.org/W1989612117","https://openalex.org/W1994257838","https://openalex.org/W2034305650","https://openalex.org/W2035060017","https://openalex.org/W2035346239","https://openalex.org/W2053715822","https://openalex.org/W2059037247","https://openalex.org/W2077565682","https://openalex.org/W2078253545","https://openalex.org/W2079493256","https://openalex.org/W2090864084","https://openalex.org/W2110026580","https://openalex.org/W2122463265","https://openalex.org/W2163731700","https://openalex.org/W2169364612","https://openalex.org/W2252189398","https://openalex.org/W2329551434","https://openalex.org/W2506243456","https://openalex.org/W2652668669","https://openalex.org/W2759660148","https://openalex.org/W2768672166","https://openalex.org/W4299993032"],"related_works":["https://openalex.org/W2009454197","https://openalex.org/W3003614869","https://openalex.org/W1973691824","https://openalex.org/W2587085640","https://openalex.org/W4386071021","https://openalex.org/W2054394682","https://openalex.org/W3089787722","https://openalex.org/W2030139799","https://openalex.org/W2288292100","https://openalex.org/W4294988587"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,31],"investigate":[4],"the":[5,19,34,73,83,86,97,102],"asymptotic":[6],"behavior":[7],"for":[8,66],"a":[9,37,42,54,92],"kind":[10],"of":[11,21,36,63,88,101],"resource":[12],"competition":[13],"model":[14],"with":[15],"environmental":[16],"noises.":[17],"Considering":[18],"impact":[20],"white":[22,89],"noise":[23,90],"on":[24,96],"birth":[25],"rate":[26,29],"and":[27,40,48,68,77,99],"death":[28],"separately,":[30],"first":[32],"prove":[33],"existence":[35],"positive":[38],"solution,":[39],"then":[41],"sufficient":[43],"condition":[44],"to":[45],"maintain":[46],"permanence":[47,98],"extinction":[49,100],"is":[50,105],"obtained":[51],"by":[52,107],"using":[53],"proper":[55],"Lyapunov":[56],"functional,":[57],"stochastic":[58,74],"comparison":[59],"theorem,":[60],"strong":[61],"law":[62],"large":[64],"numbers":[65],"martingales,":[67],"several":[69],"important":[70,94],"inequalities.":[71],"Furthermore,":[72],"final":[75],"boundedness":[76],"path":[78],"estimation":[79],"are":[80],"studied.":[81],"Finally,":[82],"fact":[84],"that":[85],"intensity":[87],"has":[91],"very":[93],"influence":[95],"system\u2019s":[103],"solution":[104],"illustrated":[106],"some":[108],"numerical":[109],"examples.":[110]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-09-26T08:19:03.415552","created_date":"2025-10-10T00:00:00"}