{"id":"https://openalex.org/W2098975400","doi":"https://doi.org/10.1155/2013/429163","title":"Positive Almost Periodic Solutions for a Discrete Competitive System Subject to Feedback Controls","display_name":"Positive Almost Periodic Solutions for a Discrete Competitive System Subject to Feedback Controls","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2098975400","doi":"https://doi.org/10.1155/2013/429163","mag":"2098975400"},"language":"en","primary_location":{"id":"doi:10.1155/2013/429163","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/429163","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/429163.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/429163.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100603531","display_name":"Qinglong Wang","orcid":"https://orcid.org/0000-0002-3074-4786"},"institutions":[{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]},{"id":"https://openalex.org/I4210106563","display_name":"Hubei University for Nationalities","ror":"https://ror.org/01q349q17","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210106563"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qinglong Wang","raw_affiliation_strings":["Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China","Key Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Hubei University for Nationalities, Enshi, Hubei 445000, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China","institution_ids":["https://openalex.org/I75900474","https://openalex.org/I4210106563"]},{"raw_affiliation_string":"Key Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Hubei University for Nationalities, Enshi, Hubei 445000, China","institution_ids":["https://openalex.org/I4210106563","https://openalex.org/I75900474"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021781386","display_name":"Zhijun Liu","orcid":"https://orcid.org/0000-0003-3383-5621"},"institutions":[{"id":"https://openalex.org/I4210106563","display_name":"Hubei University for Nationalities","ror":"https://ror.org/01q349q17","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210106563"]},{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhijun Liu","raw_affiliation_strings":["Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China","Key Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Hubei University for Nationalities, Enshi, Hubei 445000, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China","institution_ids":["https://openalex.org/I75900474","https://openalex.org/I4210106563"]},{"raw_affiliation_string":"Key Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Hubei University for Nationalities, Enshi, Hubei 445000, China","institution_ids":["https://openalex.org/I4210106563","https://openalex.org/I75900474"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010951763","display_name":"Zuxiong Li","orcid":"https://orcid.org/0000-0002-2526-8113"},"institutions":[{"id":"https://openalex.org/I4210106563","display_name":"Hubei University for Nationalities","ror":"https://ror.org/01q349q17","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210106563"]},{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zuxiong Li","raw_affiliation_strings":["Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China","institution_ids":["https://openalex.org/I75900474","https://openalex.org/I4210106563"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021781386"],"corresponding_institution_ids":["https://openalex.org/I4210106563","https://openalex.org/I75900474"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.9795,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.80170168,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"14"},"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":0.9994000196456909,"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":0.9994000196456909,"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":0.9975000023841858,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/lyapunov-function","display_name":"Lyapunov function","score":0.7000465989112854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6184697151184082},{"id":"https://openalex.org/keywords/subject","display_name":"Subject (documents)","score":0.6116998195648193},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5984723567962646},{"id":"https://openalex.org/keywords/periodic-system","display_name":"Periodic system","score":0.5648550391197205},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4814316928386688},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4605090022087097},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.4393298923969269},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40555334091186523},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3088691830635071},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3015492260456085},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.24905160069465637},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08414006233215332},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06473889946937561},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05512040853500366}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7000465989112854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6184697151184082},{"id":"https://openalex.org/C2777855551","wikidata":"https://www.wikidata.org/wiki/Q12310021","display_name":"Subject (documents)","level":2,"score":0.6116998195648193},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5984723567962646},{"id":"https://openalex.org/C2989467761","wikidata":"https://www.wikidata.org/wiki/Q10693","display_name":"Periodic system","level":2,"score":0.5648550391197205},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4814316928386688},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4605090022087097},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.4393298923969269},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40555334091186523},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3088691830635071},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3015492260456085},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.24905160069465637},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08414006233215332},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06473889946937561},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05512040853500366},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C161191863","wikidata":"https://www.wikidata.org/wiki/Q199655","display_name":"Library science","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},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2013/429163","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/429163","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/429163.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394808188","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394808188","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:429163","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/429163.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:47674bacf5a240ec97062ba2edda0b64","is_oa":true,"landing_page_url":"https://doaj.org/article/47674bacf5a240ec97062ba2edda0b64","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/429163","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/429163","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/429163.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2296587852","display_name":null,"funder_award_id":"212111","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3626265869","display_name":null,"funder_award_id":"B20111906","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4020255992","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5370843663","display_name":null,"funder_award_id":"11261017","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6255607015","display_name":null,"funder_award_id":"61261044","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6258415954","display_name":null,"funder_award_id":"Chinese","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2098975400.pdf","grobid_xml":"https://content.openalex.org/works/W2098975400.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W208467494","https://openalex.org/W1964801597","https://openalex.org/W1975563898","https://openalex.org/W1981043080","https://openalex.org/W2005733367","https://openalex.org/W2045185199","https://openalex.org/W2058707972","https://openalex.org/W2068784843","https://openalex.org/W2070207443","https://openalex.org/W2092582457","https://openalex.org/W2130220816","https://openalex.org/W2134203160","https://openalex.org/W2149013423","https://openalex.org/W2362877222"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4388258507","https://openalex.org/W2392013855","https://openalex.org/W4318064328","https://openalex.org/W2357926602","https://openalex.org/W3200517220","https://openalex.org/W2164703465","https://openalex.org/W2168383058","https://openalex.org/W2143247663","https://openalex.org/W2050693590"],"abstract_inverted_index":{"This":[0],"paper":[1],"concerns":[2],"a":[3],"discrete":[4],"competitive":[5],"system":[6,33],"subject":[7],"to":[8],"feedback":[9],"controls.":[10],"By":[11],"using":[12],"Lyapunov":[13],"function":[14],"and":[15,21],"some":[16],"preliminary":[17],"lemmas,":[18],"the":[19,32,39],"existence":[20],"uniformly":[22],"asymptotic":[23],"stability":[24],"of":[25,31,41],"unique":[26],"positive":[27],"almost":[28],"periodic":[29],"solution":[30],"are":[34],"investigated.":[35],"Numerical":[36],"simulations":[37],"suggest":[38],"feasibility":[40],"our":[42],"theoretical":[43],"results.":[44]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}
