{"id":"https://openalex.org/W7225640206","doi":"https://doi.org/10.1186/s13661-026-02386-7","title":"Effect of polluted environment on one prey and two competing predators with Gompertz growth and Beddington-DeAngelis functional response","display_name":"Effect of polluted environment on one prey and two competing predators with Gompertz growth and Beddington-DeAngelis functional response","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225640206","doi":"https://doi.org/10.1186/s13661-026-02386-7"},"language":"en","primary_location":{"id":"doi:10.1186/s13661-026-02386-7","doi":"https://doi.org/10.1186/s13661-026-02386-7","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13661-026-02386-7","pdf_url":null,"source":{"id":"https://openalex.org/S61795452","display_name":"Boundary Value Problems","issn_l":"1687-2762","issn":["1687-2762","1687-2770"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-d","norway-1","poland-40","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Boundary Value Problems","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1186/s13661-026-02386-7","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062114054","display_name":"A. Raveendra Babu","orcid":"https://orcid.org/0000-0002-8861-6779","observed_orcids":["https://orcid.org/0000-0002-8861-6779"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raveendra Babu\u00a0A.","raw_affiliation_strings":["Department of Mathematics, Prestige Institute of Management and Research, Gwalior, 474020, India"],"raw_orcid":"https://orcid.org/0000-0002-8861-6779","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Prestige Institute of Management and Research, Gwalior, 474020, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034122682","display_name":"Ausif Padder","orcid":"https://orcid.org/0000-0002-9942-908X","observed_orcids":["https://orcid.org/0000-0002-9942-908X"]},"institutions":[{"id":"https://openalex.org/I244572783","display_name":"Symbiosis International University","ror":"https://ror.org/005r2ww51","country_code":"IN","type":"education","lineage":["https://openalex.org/I244572783"]},{"id":"https://openalex.org/I4387152582","display_name":"A'Sharqiyah University","ror":"https://ror.org/044v96v72","country_code":"OM","type":"education","lineage":["https://openalex.org/I4387152582"]}],"countries":["IN","OM"],"is_corresponding":true,"raw_author_name":"Ausif Padder","raw_affiliation_strings":["Department of Basic and Applied Sciences, College of Applied and Health Sciences, A\u2019Sharqiyah University, P.O. Box 42, Ibra 400, Sultanate of Oman","Symbiosis Institute of Technology, Hyderabad Campus, Symbiosis International (Deemed University), Pune, India"],"raw_orcid":"https://orcid.org/0000-0002-9942-908X","affiliations":[{"raw_affiliation_string":"Department of Basic and Applied Sciences, College of Applied and Health Sciences, A\u2019Sharqiyah University, P.O. Box 42, Ibra 400, Sultanate of Oman","institution_ids":["https://openalex.org/I4387152582"]},{"raw_affiliation_string":"Symbiosis Institute of Technology, Hyderabad Campus, Symbiosis International (Deemed University), Pune, India","institution_ids":["https://openalex.org/I244572783"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029283044","display_name":"Kavita Makwana","orcid":"https://orcid.org/0009-0004-0479-8168","observed_orcids":["https://orcid.org/0009-0004-0479-8168"]},"institutions":[{"id":"https://openalex.org/I4405261040","display_name":"SAGE University Indore","ror":"https://ror.org/04nwq2r79","country_code":"IN","type":"education","lineage":["https://openalex.org/I4405261040"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kavita Makwana","raw_affiliation_strings":["Institute of Advanced Computing, SAGE University, Indore, 452020, India"],"raw_orcid":"https://orcid.org/0009-0004-0479-8168","affiliations":[{"raw_affiliation_string":"Institute of Advanced Computing, SAGE University, Indore, 452020, India","institution_ids":["https://openalex.org/I4405261040"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5034122682"],"corresponding_institution_ids":["https://openalex.org/I244572783","https://openalex.org/I4387152582"],"apc_list":{"value":1890,"currency":"USD","value_usd":1890},"apc_paid":{"value":1890,"currency":"USD","value_usd":1890},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":1.0,"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/T10447","display_name":"Environmental Toxicology and Ecotoxicology","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2307","display_name":"Health, Toxicology and Mutagenesis"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13377","display_name":"Ecosystem dynamics and resilience","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/environmental-pollution","display_name":"environmental pollution","score":0.5989999771118164},{"id":"https://openalex.org/keywords/toxicants","display_name":"toxicants","score":0.5249999761581421},{"id":"https://openalex.org/keywords/phytoplankton","display_name":"phytoplankton","score":0.8149999976158142},{"id":"https://openalex.org/keywords/zooplankton","display_name":"zooplankton","score":0.9430000185966492},{"id":"https://openalex.org/keywords/gompertz-growth","display_name":"Gompertz growth","score":0.9440000057220459},{"id":"https://openalex.org/keywords/beddington-deangelis-functional-response","display_name":"Beddington-DeAngelis functional response","score":0.9990000128746033},{"id":"https://openalex.org/keywords/ecotoxicology","display_name":"ecotoxicology","score":0.7129999995231628},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.8529999852180481},{"id":"https://openalex.org/keywords/oscillatory-instability","display_name":"oscillatory instability","score":0.6309999823570251},{"id":"https://openalex.org/keywords/stability-of-equilibrium","display_name":"equilibrium stability","score":0.6850000023841858},{"id":"https://openalex.org/keywords/sensitivity-analysis","display_name":"sensitivity analysis","score":0.6729999780654907},{"id":"https://openalex.org/keywords/freshwater-ecosystems","display_name":"freshwater ecosystems","score":0.8420000076293945},{"id":"https://openalex.org/keywords/coexistence","display_name":"coexistence","score":0.4569999873638153}],"concepts":[{"id":"https://openalex.org/C2780473477","wikidata":"https://www.wikidata.org/wiki/Q3072135","display_name":"Toxicant","level":3,"score":0.774399995803833},{"id":"https://openalex.org/C2780892065","wikidata":"https://www.wikidata.org/wiki/Q184755","display_name":"Phytoplankton","level":3,"score":0.7077000141143799},{"id":"https://openalex.org/C110872660","wikidata":"https://www.wikidata.org/wiki/Q37813","display_name":"Ecosystem","level":2,"score":0.6506999731063843},{"id":"https://openalex.org/C158836135","wikidata":"https://www.wikidata.org/wiki/Q842627","display_name":"Zooplankton","level":2,"score":0.6468999981880188},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.4961000084877014},{"id":"https://openalex.org/C39432304","wikidata":"https://www.wikidata.org/wiki/Q188847","display_name":"Environmental science","level":0,"score":0.4593999981880188},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.4584999978542328},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.41749998927116394},{"id":"https://openalex.org/C110201527","wikidata":"https://www.wikidata.org/wiki/Q5508845","display_name":"Functional response","level":4,"score":0.4153999984264374},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.40540000796318054},{"id":"https://openalex.org/C134463574","wikidata":"https://www.wikidata.org/wiki/Q1011785","display_name":"Gompertz function","level":2,"score":0.40369999408721924},{"id":"https://openalex.org/C64107356","wikidata":"https://www.wikidata.org/wiki/Q295046","display_name":"Ecosystem model","level":3,"score":0.39250001311302185},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.3871999979019165},{"id":"https://openalex.org/C46685645","wikidata":"https://www.wikidata.org/wiki/Q2890135","display_name":"Freshwater ecosystem","level":3,"score":0.38519999384880066},{"id":"https://openalex.org/C34506677","wikidata":"https://www.wikidata.org/wiki/Q5333257","display_name":"Ecological stability","level":3,"score":0.3393000066280365},{"id":"https://openalex.org/C521259446","wikidata":"https://www.wikidata.org/wiki/Q58734","display_name":"Pollution","level":2,"score":0.3034000098705292},{"id":"https://openalex.org/C2777181938","wikidata":"https://www.wikidata.org/wiki/Q180148","display_name":"Rotifer","level":2,"score":0.28619998693466187},{"id":"https://openalex.org/C82685317","wikidata":"https://www.wikidata.org/wiki/Q19829510","display_name":"Pollutant","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C24518262","wikidata":"https://www.wikidata.org/wiki/Q16197023","display_name":"Threatened species","level":3,"score":0.27790001034736633},{"id":"https://openalex.org/C175327387","wikidata":"https://www.wikidata.org/wiki/Q3289906","display_name":"Aquatic ecosystem","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26649999618530273},{"id":"https://openalex.org/C101991246","wikidata":"https://www.wikidata.org/wiki/Q5422078","display_name":"Extinction (optical mineralogy)","level":2,"score":0.2563999891281128}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1186/s13661-026-02386-7","doi":"https://doi.org/10.1186/s13661-026-02386-7","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13661-026-02386-7","pdf_url":null,"source":{"id":"https://openalex.org/S61795452","display_name":"Boundary Value Problems","issn_l":"1687-2762","issn":["1687-2762","1687-2770"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-d","norway-1","poland-40","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Boundary Value Problems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1186/s13661-026-02386-7","doi":"https://doi.org/10.1186/s13661-026-02386-7","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13661-026-02386-7","pdf_url":null,"source":{"id":"https://openalex.org/S61795452","display_name":"Boundary Value Problems","issn_l":"1687-2762","issn":["1687-2762","1687-2770"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-d","norway-1","poland-40","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Boundary Value Problems","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7778000235557556,"display_name":"Clean water and sanitation","id":"https://metadata.un.org/sdg/6"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4412378726","https://openalex.org/W2759991140","https://openalex.org/W2030762005","https://openalex.org/W4405662143","https://openalex.org/W2943868247","https://openalex.org/W1977064482","https://openalex.org/W4285176709","https://openalex.org/W4409748933","https://openalex.org/W4407093418","https://openalex.org/W4414166628"],"abstract_inverted_index":{"Freshwater":[0],"ecosystems":[1],"are":[2,62],"increasingly":[3],"threatened":[4],"by":[5,81],"pollutants":[6],"that":[7,24,95,127],"disrupt":[8],"species":[9],"interactions":[10,50],"and":[11,17,31,59,72,89,125,133,160,169],"ecosystem":[12,173],"stability.":[13],"This":[14],"study":[15],"develops":[16],"analyzes":[18],"a":[19,41,52,82],"nonlinear":[20],"eco-toxicological":[21],"mathematical":[22,66],"model":[23],"couples":[25],"phytoplankton,":[26],"two":[27],"competing":[28],"zooplankton":[29,100],"species,":[30],"an":[32],"environmental":[33],"toxicant.":[34],"The":[35,148],"phytoplankton":[36,60,134],"growth":[37],"is":[38],"modeled":[39],"using":[40,86],"Gompertz":[42],"function":[43],"to":[44,98,137,145],"capture":[45],"stress-driven":[46],"asymmetry,":[47],"while":[48,110],"predator\u2013prey":[49],"follow":[51],"Beddington\u2013DeAngelis":[53],"functional":[54],"response.":[55],"Toxicant":[56],"input,":[57],"decay,":[58],"uptake":[61],"incorporated":[63],"into":[64,163],"the":[65,73,99,104,114,120,151,170],"system.":[67],"We":[68],"establish":[69],"positivity,":[70],"boundedness,":[71],"existence":[74],"of":[75,122,154,172],"five":[76],"biologically":[77],"feasible":[78],"equilibria,":[79],"followed":[80],"detailed":[83],"stability":[84,115,121],"analysis":[85],"Jacobian":[87],"eigenvalues":[88],"Routh\u2013Hurwitz":[90],"criteria.":[91],"Sensitivity":[92],"indices":[93],"show":[94],"parameters":[96,112],"linked":[97],"(predator)":[101],"populations":[102],"have":[103],"strongest":[105],"influence":[106],"on":[107],"equilibrium":[108],"levels,":[109],"toxicant-related":[111],"govern":[113],"transitions.":[116],"Numerical":[117],"simulations":[118],"confirm":[119],"non-trivial":[123],"equilibria":[124],"reveal":[126],"increases":[128],"in":[129,157],"toxicant":[130,155],"input":[131],"rate":[132],"mortality":[135],"due":[136],"toxicity":[138],"can":[139],"trigger":[140],"subcritical":[141],"Hopf":[142],"bifurcations,":[143],"leading":[144],"oscillatory":[146],"instabilities.":[147],"results":[149],"underscore":[150],"ecological":[152],"importance":[153],"thresholds":[156],"freshwater":[158],"communities":[159],"provide":[161],"insight":[162],"how":[164],"pollution":[165],"influences":[166],"coexistence,":[167],"resilience,":[168],"risk":[171],"destabilization.":[174]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}