{"id":"https://openalex.org/W3210809599","doi":"https://doi.org/10.1155/2021/6209908","title":"Dynamics on Effect of Prey Refuge Proportional to Predator in Discrete\u2010Time Prey\u2010Predator Model","display_name":"Dynamics on Effect of Prey Refuge Proportional to Predator in Discrete\u2010Time Prey\u2010Predator Model","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3210809599","doi":"https://doi.org/10.1155/2021/6209908","mag":"3210809599"},"language":"en","primary_location":{"id":"doi:10.1155/2021/6209908","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/6209908","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/6209908.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","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/complexity/2021/6209908.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030722791","display_name":"G. S. Mahapatra","orcid":"https://orcid.org/0000-0002-5225-0445"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. S. Mahapatra","raw_affiliation_strings":["Department of Mathematics, National Institute of Technology Puducherry, Karaikal 609609, Puducherry, India"],"raw_orcid":"https://orcid.org/0000-0002-5225-0445","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Institute of Technology Puducherry, Karaikal 609609, Puducherry, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053894034","display_name":"P.K. Santra","orcid":"https://orcid.org/0000-0002-1857-135X"},"institutions":[{"id":"https://openalex.org/I98365261","display_name":"Indian Institute of Engineering Science and Technology, Shibpur","ror":"https://ror.org/02ytfzr55","country_code":"IN","type":"education","lineage":["https://openalex.org/I98365261"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"P. K. Santra","raw_affiliation_strings":["Abada Nsup School, Howrah 711313, West Bengal, India"],"raw_orcid":"https://orcid.org/0000-0002-1857-135X","affiliations":[{"raw_affiliation_string":"Abada Nsup School, Howrah 711313, West Bengal, India","institution_ids":["https://openalex.org/I98365261"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066581129","display_name":"Ebenezer Bonyah","orcid":"https://orcid.org/0000-0003-0808-4504"},"institutions":[{"id":"https://openalex.org/I4387154669","display_name":"Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development","ror":"https://ror.org/031d6ey43","country_code":null,"type":"education","lineage":["https://openalex.org/I4387154669"]}],"countries":["GH"],"is_corresponding":true,"raw_author_name":"Ebenezer Bonyah","raw_affiliation_strings":["Department of Mathematics Education, Akenten Appiah Menka University of Skills Training and Entrepreneurial Development, Kumasi, Ghana"],"raw_orcid":"https://orcid.org/0000-0003-0808-4504","affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, Akenten Appiah Menka University of Skills Training and Entrepreneurial Development, Kumasi, Ghana","institution_ids":["https://openalex.org/I4387154669"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066581129"],"corresponding_institution_ids":["https://openalex.org/I4387154669"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":1.7768,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.85283913,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"2021","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":0.9998000264167786,"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9955000281333923,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9736999869346619,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/predation","display_name":"Predation","score":0.8008682131767273},{"id":"https://openalex.org/keywords/predator","display_name":"Predator","score":0.6344256401062012},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.576958417892456},{"id":"https://openalex.org/keywords/functional-response","display_name":"Functional response","score":0.5396163463592529},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.5162718296051025},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5142874121665955},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4720260202884674},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.4553620219230652},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.43521714210510254},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4047647714614868},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.33167189359664917},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.17803379893302917},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16887959837913513},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13584408164024353},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10947674512863159},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10230827331542969},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.06396132707595825},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05738753080368042},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.05549696087837219}],"concepts":[{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.8008682131767273},{"id":"https://openalex.org/C96857902","wikidata":"https://www.wikidata.org/wiki/Q2138108","display_name":"Predator","level":3,"score":0.6344256401062012},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.576958417892456},{"id":"https://openalex.org/C110201527","wikidata":"https://www.wikidata.org/wiki/Q5508845","display_name":"Functional response","level":4,"score":0.5396163463592529},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.5162718296051025},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5142874121665955},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4720260202884674},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.4553620219230652},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.43521714210510254},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4047647714614868},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.33167189359664917},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.17803379893302917},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16887959837913513},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13584408164024353},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10947674512863159},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10230827331542969},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.06396132707595825},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05738753080368042},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.05549696087837219},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2021/6209908","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/6209908","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/6209908.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:21c62578b8284c559ea23d8b49a43824","is_oa":true,"landing_page_url":"https://doaj.org/article/21c62578b8284c559ea23d8b49a43824","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":"Complexity, Vol 2021 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2021/6209908","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/6209908","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/6209908.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5400000214576721,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3210809599.pdf","grobid_xml":"https://content.openalex.org/works/W3210809599.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W1991993422","https://openalex.org/W2021440629","https://openalex.org/W2096806219","https://openalex.org/W2339190293","https://openalex.org/W2531530510","https://openalex.org/W2588275666","https://openalex.org/W2600628874","https://openalex.org/W2615157158","https://openalex.org/W2730283497","https://openalex.org/W2737612165","https://openalex.org/W2789840218","https://openalex.org/W2794396883","https://openalex.org/W2795844075","https://openalex.org/W2809619817","https://openalex.org/W2888976400","https://openalex.org/W2898839368","https://openalex.org/W2900205358","https://openalex.org/W2903942731","https://openalex.org/W2923336894","https://openalex.org/W2938710160","https://openalex.org/W2938873725","https://openalex.org/W2940924658","https://openalex.org/W2987982387","https://openalex.org/W2997091409","https://openalex.org/W3000104042","https://openalex.org/W3000900117","https://openalex.org/W3010644882","https://openalex.org/W3010740850","https://openalex.org/W3013075322","https://openalex.org/W3016874765","https://openalex.org/W3034961454","https://openalex.org/W3035336839","https://openalex.org/W3037067795","https://openalex.org/W3041890084","https://openalex.org/W3043397340","https://openalex.org/W3043783004","https://openalex.org/W3082800164","https://openalex.org/W3103408287","https://openalex.org/W3196055909"],"related_works":["https://openalex.org/W2061879675","https://openalex.org/W4233887507","https://openalex.org/W2084621533","https://openalex.org/W2077303587","https://openalex.org/W2059261737","https://openalex.org/W2054969521","https://openalex.org/W3033051025","https://openalex.org/W3194003107","https://openalex.org/W2039016328","https://openalex.org/W2073664375"],"abstract_inverted_index":{"Prey\u2010predator":[0],"models":[1],"with":[2,90],"refuge":[3,14,16,26,38,46,80,100,146,163],"effect":[4,84,160],"have":[5],"great":[6],"importance":[7],"in":[8,27,85],"the":[9,21,28,50,54,76,91,104,108,125,137,145,149,159],"context":[10],"of":[11,25,37,78,111,118,127,148,161],"ecology.":[12],"Constant":[13],"and":[15,65,116,130,140],"proportional":[17,48,81],"to":[18,49,53,82,143],"prey":[19,69,79,128,162],"are":[20,33,132],"most":[22],"popular":[23],"concepts":[24,39],"existing":[29],"literature.":[30],"Now,":[31],"there":[32],"new":[34],"different":[35],"types":[36],"attracting":[40],"researchers.":[41],"This":[42,134],"study":[43],"considers":[44],"a":[45,86],"concept":[47],"predator":[51,83],"due":[52],"fear":[55],"induced":[56],"by":[57],"predators.":[58],"When":[59],"predators":[60],"increase,":[61],"fears":[62],"also":[63,71],"increase":[64],"that":[66],"is":[67,107],"why":[68],"refuges":[70],"increase.":[72],"Here,":[73],"we":[74],"examine":[75],"influence":[77,126],"discrete":[87,153],"prey\u2010predator":[88],"interaction":[89],"Holling":[92],"type":[93],"II":[94],"functional":[95],"response":[96],"model.":[97,150],"Is":[98],"this":[99,112],"stabilizing":[101],"or":[102],"destabilizing":[103],"system?":[105],"That":[106],"central":[109],"question":[110],"study.":[113],"The":[114,151],"existence":[115],"stability":[117],"fixed":[119],"points,":[120],"Period\u2010Doubling":[121],"Bifurcation,":[122,124],"Neimark\u2013Sacker":[123],"refuge,":[129],"chaos":[131],"analyzed.":[133],"work":[135],"provides":[136],"bifurcation":[138],"diagrams":[139],"Lyapunov":[141],"exponents":[142],"analyze":[144],"parameter":[147],"proposed":[152],"model":[154],"indicates":[155],"rich":[156],"dynamics":[157],"as":[158],"through":[164],"numerical":[165],"simulations.":[166]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
