{"id":"https://openalex.org/W3040750168","doi":"https://doi.org/10.1109/access.2020.3008522","title":"Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model","display_name":"Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3040750168","doi":"https://doi.org/10.1109/access.2020.3008522","mag":"3040750168"},"language":"en","primary_location":{"id":"doi:10.1109/access.2020.3008522","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3008522","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09138422.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09138422.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002572812","display_name":"Youping Lin","orcid":"https://orcid.org/0000-0001-8243-9612"},"institutions":[{"id":"https://openalex.org/I161346416","display_name":"Jimei University","ror":"https://ror.org/03hknyb50","country_code":"CN","type":"education","lineage":["https://openalex.org/I161346416"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Youping Lin","raw_affiliation_strings":["Chengyi University College, Jimei University, Xiamen, China"],"raw_orcid":"https://orcid.org/0000-0001-8243-9612","affiliations":[{"raw_affiliation_string":"Chengyi University College, Jimei University, Xiamen, China","institution_ids":["https://openalex.org/I161346416"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024827048","display_name":"Qamar Din","orcid":null},"institutions":[{"id":"https://openalex.org/I4387154749","display_name":"University of Poonch Rawalakot","ror":"https://ror.org/045arbm30","country_code":null,"type":"education","lineage":["https://openalex.org/I4387154749"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Qamar Din","raw_affiliation_strings":["Department of Mathematics, University of Poonch Rawalakot, Rawalakot, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-0999-7404","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Poonch Rawalakot, Rawalakot, Pakistan","institution_ids":["https://openalex.org/I4387154749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028967774","display_name":"Muhammad Rafaqat","orcid":"https://orcid.org/0000-0002-7437-5994"},"institutions":[{"id":"https://openalex.org/I142204992","display_name":"University of Lahore","ror":"https://ror.org/051jrjw38","country_code":"PK","type":"education","lineage":["https://openalex.org/I142204992"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Rafaqat","raw_affiliation_strings":["Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-7437-5994","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan","institution_ids":["https://openalex.org/I142204992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103005668","display_name":"Abdelalim A. Elsadany","orcid":"https://orcid.org/0000-0001-5365-5316"},"institutions":[{"id":"https://openalex.org/I114794399","display_name":"Suez Canal University","ror":"https://ror.org/02m82p074","country_code":"EG","type":"education","lineage":["https://openalex.org/I114794399"]},{"id":"https://openalex.org/I142608572","display_name":"Prince Sattam Bin Abdulaziz University","ror":"https://ror.org/04jt46d36","country_code":"SA","type":"education","lineage":["https://openalex.org/I142608572"]}],"countries":["EG","SA"],"is_corresponding":false,"raw_author_name":"Abdelalim A. Elsadany","raw_affiliation_strings":["Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt","Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-5365-5316","affiliations":[{"raw_affiliation_string":"Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt","institution_ids":["https://openalex.org/I114794399"]},{"raw_affiliation_string":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia","institution_ids":["https://openalex.org/I142608572"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102843460","display_name":"Yanqiu Zeng","orcid":"https://orcid.org/0000-0003-4656-359X"},"institutions":[{"id":"https://openalex.org/I161346416","display_name":"Jimei University","ror":"https://ror.org/03hknyb50","country_code":"CN","type":"education","lineage":["https://openalex.org/I161346416"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanqiu Zeng","raw_affiliation_strings":["Chengyi University College, Jimei University, Xiamen, China"],"raw_orcid":"https://orcid.org/0000-0003-4656-359X","affiliations":[{"raw_affiliation_string":"Chengyi University College, Jimei University, Xiamen, China","institution_ids":["https://openalex.org/I161346416"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5002572812"],"corresponding_institution_ids":["https://openalex.org/I161346416"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":3.2357,"has_fulltext":true,"cited_by_count":33,"citation_normalized_percentile":{"value":0.92720158,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"8","issue":null,"first_page":"126760","last_page":"126775"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.8041098117828369},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.6040921807289124},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.5730592608451843},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5680391192436218},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5267062783241272},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5186514258384705},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5034920573234558},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49586519598960876},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47415488958358765},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.43991583585739136},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.43596014380455017},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4321902394294739},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.4270494878292084},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.4262455701828003},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.42420676350593567},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4192250669002533},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.4029185473918915},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3084784746170044},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2467004656791687},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10334062576293945}],"concepts":[{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.8041098117828369},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.6040921807289124},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.5730592608451843},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5680391192436218},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5267062783241272},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5186514258384705},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5034920573234558},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49586519598960876},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47415488958358765},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.43991583585739136},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.43596014380455017},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4321902394294739},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.4270494878292084},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.4262455701828003},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.42420676350593567},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4192250669002533},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.4029185473918915},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3084784746170044},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2467004656791687},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10334062576293945},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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":2,"locations":[{"id":"doi:10.1109/access.2020.3008522","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3008522","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09138422.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a1e58b5ddc76461bbdaba204748000dc","is_oa":true,"landing_page_url":"https://doaj.org/article/a1e58b5ddc76461bbdaba204748000dc","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":"IEEE Access, Vol 8, Pp 126760-126775 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2020.3008522","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3008522","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09138422.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3040750168.pdf","grobid_xml":"https://content.openalex.org/works/W3040750168.grobid-xml"},"referenced_works_count":71,"referenced_works":["https://openalex.org/W126388413","https://openalex.org/W297325920","https://openalex.org/W1526544699","https://openalex.org/W1589876408","https://openalex.org/W1769306030","https://openalex.org/W1963541305","https://openalex.org/W1964801597","https://openalex.org/W1969672820","https://openalex.org/W1985534580","https://openalex.org/W1986487529","https://openalex.org/W1994100609","https://openalex.org/W2000071648","https://openalex.org/W2008691667","https://openalex.org/W2013160272","https://openalex.org/W2014613576","https://openalex.org/W2025904721","https://openalex.org/W2027665073","https://openalex.org/W2028547335","https://openalex.org/W2030728270","https://openalex.org/W2034501699","https://openalex.org/W2035379472","https://openalex.org/W2037040695","https://openalex.org/W2038947131","https://openalex.org/W2052032306","https://openalex.org/W2052125279","https://openalex.org/W2065705412","https://openalex.org/W2072583653","https://openalex.org/W2089876099","https://openalex.org/W2102472772","https://openalex.org/W2150945311","https://openalex.org/W2304096355","https://openalex.org/W2314686048","https://openalex.org/W2331625639","https://openalex.org/W2336611885","https://openalex.org/W2344298532","https://openalex.org/W2472348908","https://openalex.org/W2507897087","https://openalex.org/W2531530510","https://openalex.org/W2535820282","https://openalex.org/W2565584316","https://openalex.org/W2568356606","https://openalex.org/W2586460567","https://openalex.org/W2594650004","https://openalex.org/W2730283497","https://openalex.org/W2739445793","https://openalex.org/W2770069845","https://openalex.org/W2800424298","https://openalex.org/W2802743206","https://openalex.org/W2803802085","https://openalex.org/W2833428532","https://openalex.org/W2885662586","https://openalex.org/W2886981579","https://openalex.org/W2890649971","https://openalex.org/W2901547378","https://openalex.org/W2917019424","https://openalex.org/W2944551688","https://openalex.org/W2953792648","https://openalex.org/W2962611527","https://openalex.org/W2994914341","https://openalex.org/W2996042560","https://openalex.org/W2996237187","https://openalex.org/W3015157245","https://openalex.org/W3026733313","https://openalex.org/W3040940214","https://openalex.org/W4241290540","https://openalex.org/W4285719527","https://openalex.org/W4297918182","https://openalex.org/W4310301864","https://openalex.org/W6698959889","https://openalex.org/W6703284080","https://openalex.org/W6725663324"],"related_works":["https://openalex.org/W2546487931","https://openalex.org/W2404180431","https://openalex.org/W2803928976","https://openalex.org/W2331733846","https://openalex.org/W2348340245","https://openalex.org/W3138146974","https://openalex.org/W3097933399","https://openalex.org/W4214875847","https://openalex.org/W2059079934","https://openalex.org/W2361529576"],"abstract_inverted_index":{"Bifurcation":[0],"theory":[1,104],"(center":[2],"manifold":[3,107],"and":[4,20,52,60,105,114,118,133,147],"Ljapunov-Schmidt":[5],"reduction,":[6],"normal":[7],"form":[8],"theory,":[9],"universal":[10],"unfolding,":[11],"calculation":[12],"of":[13,27,34,43,75,90,102,116],"bifurcation":[14,103],"diagrams)":[15],"has":[16,57],"become":[17],"an":[18],"important":[19],"very":[21],"useful":[22],"means":[23],"in":[24,31],"the":[25,72,100],"solution":[26],"nonlinear":[28],"stability":[29],"problems":[30],"many":[32],"branches":[33],"engineering.":[35],"The":[36,54,86],"present":[37],"study":[38],"deals":[39],"with":[40,80,99],"qualitative":[41,73],"behavior":[42,63,74,89],"a":[44,76],"two-dimensional":[45],"discrete-time":[46,55,77,95],"system":[47],"for":[48,84,94,112],"interaction":[49],"between":[50],"prey":[51],"predator.":[53],"model":[56,79],"more":[58],"chaotic":[59],"rich":[61],"dynamical":[62],"as":[64],"compare":[65],"to":[66,143],"its":[67],"continuous":[68],"counterpart.":[69],"We":[70],"investigate":[71],"Lotka-Volterra":[78,96],"linear":[81],"functional":[82],"response":[83],"prey.":[85],"local":[87],"asymptotic":[88],"equilibria":[91],"is":[92],"discussed":[93],"model.":[97],"Furthermore,":[98],"help":[101],"center":[106],"theorem,":[108],"explicit":[109],"parametric":[110],"conditions":[111],"directions":[113],"existence":[115],"flip":[117],"Hopf":[119],"bifurcations":[120],"are":[121,137,141],"investigated.":[122],"Moreover,":[123],"two":[124],"chaos":[125],"control":[126,132,135],"methods,":[127],"that":[128],"is,":[129],"OGY":[130],"feedback":[131],"hybrid":[134],"strategy,":[136],"implemented.":[138],"Numerical":[139],"simulations":[140],"provided":[142],"illustrate":[144],"theoretical":[145],"discussion":[146],"their":[148],"effectiveness.":[149]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":5}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}