{"id":"https://openalex.org/W4401174097","doi":"https://doi.org/10.1142/s0218127424501207","title":"Complex Dynamics of a Discretized Predator\u2013Prey System with Prey Refuge Using a Piecewise Constant Argument Method","display_name":"Complex Dynamics of a Discretized Predator\u2013Prey System with Prey Refuge Using a Piecewise Constant Argument Method","publication_year":2024,"publication_date":"2024-07-31","ids":{"openalex":"https://openalex.org/W4401174097","doi":"https://doi.org/10.1142/s0218127424501207"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127424501207","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127424501207","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5016560359","display_name":"Rizwan Ahmed","orcid":"https://orcid.org/0000-0002-4900-0488"},"institutions":[{"id":"https://openalex.org/I899713450","display_name":"Air University","ror":"https://ror.org/03yfe9v83","country_code":"PK","type":"education","lineage":["https://openalex.org/I899713450"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Rizwan Ahmed","raw_affiliation_strings":["Department of Mathematics, Air University Multan Campus, Bahawalpur Road, Multan, Punjab, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-4900-0488","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Air University Multan Campus, Bahawalpur Road, Multan, Punjab, Pakistan","institution_ids":["https://openalex.org/I899713450"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052541435","display_name":"Abdul Qadeer Khan","orcid":"https://orcid.org/0000-0002-0278-1352"},"institutions":[{"id":"https://openalex.org/I146840658","display_name":"University of Azad Jammu and Kashmir","ror":"https://ror.org/015566d55","country_code":"PK","type":"education","lineage":["https://openalex.org/I146840658"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Abdul Qadeer Khan","raw_affiliation_strings":["Department of Mathematics, The University of Azad Jammu and Kashmir, Muzaffarabad 13100, Azad Jammu and Kashmir, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-0278-1352","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Azad Jammu and Kashmir, Muzaffarabad 13100, Azad Jammu and Kashmir, Pakistan","institution_ids":["https://openalex.org/I146840658"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103516438","display_name":"Muhammad Amer","orcid":null},"institutions":[{"id":"https://openalex.org/I899713450","display_name":"Air University","ror":"https://ror.org/03yfe9v83","country_code":"PK","type":"education","lineage":["https://openalex.org/I899713450"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Amer","raw_affiliation_strings":["Department of Mathematics, Air University Multan Campus, Bahawalpur Road, Multan, Punjab, Pakistan"],"raw_orcid":"https://orcid.org/0009-0008-5648-1989","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Air University Multan Campus, Bahawalpur Road, Multan, Punjab, Pakistan","institution_ids":["https://openalex.org/I899713450"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106160955","display_name":"Aniqa Faizan","orcid":"https://orcid.org/0009-0005-3575-2434"},"institutions":[{"id":"https://openalex.org/I4210102737","display_name":"Khwaja Fareed University of Engineering and Information Technology","ror":"https://ror.org/0161dyt30","country_code":"PK","type":"education","lineage":["https://openalex.org/I4210102737"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Aniqa Faizan","raw_affiliation_strings":["Department of Mathematics, Khawaja Fareed University of Engineering and Information Technology, Abu Dhabi Road, Rahim Yar Khan, Punjab, Pakistan"],"raw_orcid":"https://orcid.org/0009-0005-3575-2434","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Khawaja Fareed University of Engineering and Information Technology, Abu Dhabi Road, Rahim Yar Khan, Punjab, Pakistan","institution_ids":["https://openalex.org/I4210102737"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112733422","display_name":"Imtiaz Ahmed","orcid":null},"institutions":[{"id":"https://openalex.org/I69716792","display_name":"Mirpur University of Science and Technology","ror":"https://ror.org/04qjkhc08","country_code":"PK","type":"education","lineage":["https://openalex.org/I69716792"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Imtiaz Ahmed","raw_affiliation_strings":["Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur 10250, Azad Jammu and Kashmir, Pakistan"],"raw_orcid":"https://orcid.org/0000-0003-3206-1900","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur 10250, Azad Jammu and Kashmir, Pakistan","institution_ids":["https://openalex.org/I69716792"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.3173,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.96022829,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"34","issue":"10","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":0.9970999956130981,"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":0.9970999956130981,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9767000079154968,"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"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9315000176429749,"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/constant","display_name":"Constant (computer programming)","score":0.7561114430427551},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7166004776954651},{"id":"https://openalex.org/keywords/predation","display_name":"Predation","score":0.7069607377052307},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.646581768989563},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5773040652275085},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.4980647563934326},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.4401860535144806},{"id":"https://openalex.org/keywords/predator","display_name":"Predator","score":0.43739446997642517},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3974747061729431},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3354499340057373},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.2869614362716675},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22633662819862366},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1944502592086792},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14781004190444946},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.13589057326316833},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1206577718257904},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.05488583445549011}],"concepts":[{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.7561114430427551},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7166004776954651},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.7069607377052307},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.646581768989563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5773040652275085},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.4980647563934326},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.4401860535144806},{"id":"https://openalex.org/C96857902","wikidata":"https://www.wikidata.org/wiki/Q2138108","display_name":"Predator","level":3,"score":0.43739446997642517},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3974747061729431},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3354499340057373},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.2869614362716675},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22633662819862366},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1944502592086792},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14781004190444946},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.13589057326316833},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1206577718257904},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.05488583445549011},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127424501207","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127424501207","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W610924978","https://openalex.org/W1969027200","https://openalex.org/W1983173496","https://openalex.org/W1984184643","https://openalex.org/W1997297480","https://openalex.org/W2001451047","https://openalex.org/W2025904721","https://openalex.org/W2035379472","https://openalex.org/W2065705412","https://openalex.org/W2069119945","https://openalex.org/W2075412394","https://openalex.org/W2086777229","https://openalex.org/W2089876099","https://openalex.org/W2099535774","https://openalex.org/W2293912636","https://openalex.org/W2323873405","https://openalex.org/W2905673345","https://openalex.org/W2940120777","https://openalex.org/W2950552189","https://openalex.org/W2954713868","https://openalex.org/W2996714137","https://openalex.org/W2997091409","https://openalex.org/W3000900117","https://openalex.org/W3010740850","https://openalex.org/W3034172508","https://openalex.org/W3041890084","https://openalex.org/W3082800164","https://openalex.org/W3084151896","https://openalex.org/W3118673363","https://openalex.org/W3133872295","https://openalex.org/W3149323513","https://openalex.org/W3196055909","https://openalex.org/W3196852277","https://openalex.org/W3208083225","https://openalex.org/W3210809599","https://openalex.org/W3216377234","https://openalex.org/W4220664834","https://openalex.org/W4225854295","https://openalex.org/W4229334190","https://openalex.org/W4230976146","https://openalex.org/W4236990395","https://openalex.org/W4244248002","https://openalex.org/W4288039073","https://openalex.org/W4294967943","https://openalex.org/W4296836720","https://openalex.org/W4297918182","https://openalex.org/W4303613946","https://openalex.org/W4366811207","https://openalex.org/W4377289618","https://openalex.org/W4379986392"],"related_works":["https://openalex.org/W2168669462","https://openalex.org/W2192426841","https://openalex.org/W2067000585","https://openalex.org/W4323811225","https://openalex.org/W2164070575","https://openalex.org/W4311356582","https://openalex.org/W2289298756","https://openalex.org/W2073795128","https://openalex.org/W2143533297","https://openalex.org/W2075391697"],"abstract_inverted_index":{"The":[0,60,119],"objective":[1],"of":[2,11,19,35,54,100],"this":[3],"work":[4],"is":[5,27,41],"to":[6,29,43,68,79,105],"investigate":[7],"the":[8,17,31,39,52,70,88,91,101,128],"complex":[9,135],"dynamics":[10],"a":[12,134],"discrete":[13,120],"predator\u2013prey":[14],"system":[15,40,102],"using":[16],"method":[18],"piecewise":[20],"constant":[21],"argument":[22],"for":[23],"discretization.":[24],"An":[25],"analysis":[26],"conducted":[28],"examine":[30],"presence":[32],"and":[33,47,57,62,73,85,113,131,136],"stability":[34],"fixed":[36],"points.":[37],"Furthermore,":[38],"shown":[42],"undergo":[44],"period-doubling":[45],"(PD)":[46],"Neimark\u2013Sacker":[48],"(NS)":[49],"bifurcations":[50],"by":[51,96],"use":[53],"center":[55],"manifold":[56],"bifurcation":[58,84,111],"theories.":[59],"feedback":[61],"hybrid":[63],"control":[64],"strategies":[65,77],"are":[66,94,103],"used":[67],"regulate":[69],"system\u2019s":[71],"bifurcating":[72],"chaotic":[74,137],"behaviors.":[75],"Both":[76],"seem":[78],"be":[80],"effective":[81],"in":[82,127],"managing":[83],"chaos":[86],"inside":[87],"system.":[89,138],"Finally,":[90],"main":[92],"results":[93],"validated":[95],"numerical":[97,129],"evidence.":[98],"Parameters":[99],"varied":[104],"produce":[106],"time":[107],"graphs,":[108,132],"phase":[109],"portraits,":[110],"diagrams,":[112],"maximum":[114],"Lyapunov":[115],"exponent":[116],"(MLE)":[117],"graphs.":[118],"model":[121],"displays":[122],"rich":[123],"dynamics,":[124],"as":[125],"seen":[126],"simulations":[130],"indicating":[133]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-09T05:49:46.723101","created_date":"2025-10-10T00:00:00"}