{"id":"https://openalex.org/W2346430432","doi":"https://doi.org/10.1080/00207160.2015.1130825","title":"Fractal analysis and control in the predator\u2013prey model","display_name":"Fractal analysis and control in the predator\u2013prey model","publication_year":2016,"publication_date":"2016-01-07","ids":{"openalex":"https://openalex.org/W2346430432","doi":"https://doi.org/10.1080/00207160.2015.1130825","mag":"2346430432"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2015.1130825","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1130825","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101971087","display_name":"Weihua Sun","orcid":"https://orcid.org/0000-0001-7924-5585"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Weihua Sun","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100714504","display_name":"Yongping Zhang","orcid":"https://orcid.org/0000-0002-8112-830X"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongping Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100327363","display_name":"Xin Zhang","orcid":"https://orcid.org/0000-0001-8475-6662"},"institutions":[{"id":"https://openalex.org/I59483232","display_name":"Shandong University of Finance and Economics","ror":"https://ror.org/02e2nnq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I59483232"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin Zhang","raw_affiliation_strings":["School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China","institution_ids":["https://openalex.org/I59483232"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101971087"],"corresponding_institution_ids":["https://openalex.org/I154099455"],"apc_list":null,"apc_paid":null,"fwci":1.8241,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.87180804,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"94","issue":"4","first_page":"737","last_page":"746"},"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":0.9919000267982483,"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":0.9919000267982483,"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/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9878000020980835,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9174000024795532,"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/julia-set","display_name":"Julia set","score":0.8726933002471924},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.6277885437011719},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6204473376274109},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5944528579711914},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5532674789428711},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.45014646649360657},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.41950908303260803},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41334325075149536},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.296097993850708},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20560386776924133}],"concepts":[{"id":"https://openalex.org/C187619975","wikidata":"https://www.wikidata.org/wiki/Q848427","display_name":"Julia set","level":2,"score":0.8726933002471924},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.6277885437011719},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6204473376274109},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5944528579711914},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5532674789428711},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.45014646649360657},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.41950908303260803},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41334325075149536},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.296097993850708},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20560386776924133},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2015.1130825","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1130825","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8520264706","display_name":null,"funder_award_id":"11501328,61403231","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":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W39945531","https://openalex.org/W54035425","https://openalex.org/W1970878995","https://openalex.org/W1994890694","https://openalex.org/W2020003671","https://openalex.org/W2024881558","https://openalex.org/W2030542169","https://openalex.org/W2032121576","https://openalex.org/W2044773904","https://openalex.org/W2045315908","https://openalex.org/W2049702703","https://openalex.org/W2066080529","https://openalex.org/W2085728653","https://openalex.org/W2086044311","https://openalex.org/W2089922075","https://openalex.org/W2127979164","https://openalex.org/W2145258006","https://openalex.org/W2149444807","https://openalex.org/W2150512555","https://openalex.org/W2206053052","https://openalex.org/W2317771247","https://openalex.org/W2331625639","https://openalex.org/W2347322126","https://openalex.org/W4230451458","https://openalex.org/W4297918182"],"related_works":["https://openalex.org/W2169256438","https://openalex.org/W3022050839","https://openalex.org/W3016642159","https://openalex.org/W109862761","https://openalex.org/W4200163514","https://openalex.org/W2910981280","https://openalex.org/W2109945488","https://openalex.org/W3002199636","https://openalex.org/W3212002927","https://openalex.org/W4321499576"],"abstract_inverted_index":{"The":[0,78],"two-dimensional":[1],"predator\u2013prey":[2],"Lotka\u2013Volterra":[3],"model":[4,21,60],"is":[5,22,29,49],"discussed":[6],"from":[7],"the":[8,16,20,25,33,38,41,45,59,81],"point":[9,48],"of":[10,15,19,44,58,83],"fractal":[11],"theory.":[12],"Julia":[13,34,39,56,72],"set":[14,73],"discrete":[17],"version":[18],"introduced.":[23],"Then,":[24],"linear":[26],"feedback":[27],"control":[28,32],"taken":[30],"to":[31,69,75],"set.":[35],"By":[36],"controlling":[37],"set,":[40],"attractive":[42,46],"domain":[43],"fixed":[47],"controlled":[50],"indirectly.":[51],"To":[52],"associate":[53],"two":[54],"different":[55,62],"sets":[57],"with":[61],"parameters,":[63],"nonlinear":[64],"coupling":[65],"items":[66],"are":[67],"designed":[68],"make":[70],"one":[71],"change":[74],"be":[76],"another.":[77],"simulations":[79],"illustrate":[80],"efficacy":[82],"these":[84],"methods.":[85]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}