{"id":"https://openalex.org/W2225374723","doi":"https://doi.org/10.1142/s0218127415300396","title":"Bifurcation Structures in a Family of 1D Discontinuous Linear-Hyperbolic Invertible Maps","display_name":"Bifurcation Structures in a Family of 1D Discontinuous Linear-Hyperbolic Invertible Maps","publication_year":2015,"publication_date":"2015-12-15","ids":{"openalex":"https://openalex.org/W2225374723","doi":"https://doi.org/10.1142/s0218127415300396","mag":"2225374723"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127415300396","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127415300396","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/A5005072286","display_name":"Roya Makrooni","orcid":"https://orcid.org/0000-0002-0838-8631"},"institutions":[{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Roya Makrooni","raw_affiliation_strings":["Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran","institution_ids":["https://openalex.org/I48379061"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045586765","display_name":"Laura Gardini","orcid":"https://orcid.org/0000-0002-3386-6543"},"institutions":[{"id":"https://openalex.org/I190397597","display_name":"University of Urbino","ror":"https://ror.org/04q4kt073","country_code":"IT","type":"education","lineage":["https://openalex.org/I190397597"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Laura Gardini","raw_affiliation_strings":["DESP University of Urbino Carlo Bo, Urbino, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DESP University of Urbino Carlo Bo, Urbino, Italy","institution_ids":["https://openalex.org/I190397597"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085576419","display_name":"Iryna Sushko","orcid":"https://orcid.org/0000-0001-5879-0699"},"institutions":[{"id":"https://openalex.org/I108970525","display_name":"Kyiv School of Economics","ror":"https://ror.org/006kf9d11","country_code":"UA","type":"education","lineage":["https://openalex.org/I108970525"]},{"id":"https://openalex.org/I190444043","display_name":"Institute of Mathematics","ror":"https://ror.org/04q3mp532","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I190444043"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Iryna Sushko","raw_affiliation_strings":["Institute of Mathematics, NASU, and Kyiv School of Economics, Kyiv, Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, NASU, and Kyiv School of Economics, Kyiv, Ukraine","institution_ids":["https://openalex.org/I108970525","https://openalex.org/I190444043"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045586765"],"corresponding_institution_ids":["https://openalex.org/I190397597"],"apc_list":null,"apc_paid":null,"fwci":2.1151,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.86527859,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"25","issue":"13","first_page":"1530039","last_page":"1530039"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9998999834060669,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9987000226974487,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mathematics","display_name":"Mathematics","score":0.7756391763687134},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6172263026237488},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.6132885813713074},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.6028470396995544},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5686913728713989},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.5598642230033875},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.4552844762802124},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.4416015148162842},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.4120425581932068},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3310578763484955},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1526462435722351}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7756391763687134},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6172263026237488},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.6132885813713074},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.6028470396995544},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5686913728713989},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.5598642230033875},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.4552844762802124},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.4416015148162842},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.4120425581932068},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3310578763484955},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1526462435722351},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127415300396","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127415300396","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"},{"id":"pmh:oai:ora.uniurb.it:11576/2631495","is_oa":false,"landing_page_url":"http://hdl.handle.net/11576/2631495","pdf_url":null,"source":{"id":"https://openalex.org/S4377196377","display_name":"CINECA IRIS Institutional Research information system (University of Urbino)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190397597","host_organization_name":"University of Urbino","host_organization_lineage":["https://openalex.org/I190397597"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W250423424","https://openalex.org/W571130116","https://openalex.org/W597801117","https://openalex.org/W658567699","https://openalex.org/W1494104450","https://openalex.org/W1502256235","https://openalex.org/W1543746018","https://openalex.org/W1552277675","https://openalex.org/W1849491987","https://openalex.org/W1918015919","https://openalex.org/W1968102739","https://openalex.org/W1968276462","https://openalex.org/W1970311793","https://openalex.org/W1974520525","https://openalex.org/W1979401712","https://openalex.org/W2000811362","https://openalex.org/W2005988040","https://openalex.org/W2011227277","https://openalex.org/W2015243509","https://openalex.org/W2019383201","https://openalex.org/W2020783811","https://openalex.org/W2023319414","https://openalex.org/W2042192623","https://openalex.org/W2049203971","https://openalex.org/W2056049153","https://openalex.org/W2059380896","https://openalex.org/W2080761408","https://openalex.org/W2089064840","https://openalex.org/W2127666064","https://openalex.org/W2138489795","https://openalex.org/W2143976842","https://openalex.org/W2147816319","https://openalex.org/W2159251357","https://openalex.org/W2164090485","https://openalex.org/W2168978595","https://openalex.org/W2170408252","https://openalex.org/W2484469314","https://openalex.org/W2487413971","https://openalex.org/W2500622636","https://openalex.org/W2795407492","https://openalex.org/W4234277200","https://openalex.org/W4240452402"],"related_works":["https://openalex.org/W2546487931","https://openalex.org/W2325048728","https://openalex.org/W56905705","https://openalex.org/W2775656422","https://openalex.org/W2978098199","https://openalex.org/W2003334682","https://openalex.org/W2024878967","https://openalex.org/W2054978396","https://openalex.org/W3042510364","https://openalex.org/W2923981205"],"abstract_inverted_index":{"We":[0,98],"consider":[1],"a":[2,18,23,66,82,126,148],"family":[3],"of":[4,31,36,95,111,125,140,204],"one-dimensional":[5],"discontinuous":[6],"invertible":[7],"maps":[8],"from":[9,58,77],"an":[10],"application":[11],"in":[12,103],"engineering.":[13],"It":[14],"is":[15,75,158,172,185],"defined":[16],"by":[17,22],"linear":[19],"function":[20,25],"and":[21,33,160,174],"hyperbolic":[24,38,113],"with":[26,169,202],"real":[27],"exponent.":[28],"The":[29],"presence":[30],"vertical":[32],"horizontal":[34],"asymptotes":[35,94],"the":[37,51,55,62,71,78,93,96,100,104,109,112,123,141,156,165,175,183,190,199,210],"branch":[39],"leads":[40],"to":[41,92,132,147],"particular":[42],"codimension-two":[43],"border":[44],"collision":[45],"bifurcation":[46,56,73,101],"(BCB)":[47],"such":[48],"that":[49],"if":[50,70,155,182],"parameter":[52,105],"point":[53],"approaches":[54],"value":[57,74],"one":[59],"side":[60,80],"then":[61,81,164,189],"related":[63,91,130,142,191],"cycle":[64],"undergoes":[65],"regular":[67,149],"BCB,":[68],"while":[69,181],"same":[72],"approached":[76],"other":[79],"nonregular":[83,151],"BCB":[84],"occurs,":[85],"involving":[86],"periodic":[87],"points":[88],"at":[89],"infinity,":[90],"map.":[97],"investigate":[99],"structure":[102,168],"space.":[106],"Depending":[107],"on":[108],"exponent":[110,157,184],"branch,":[114],"different":[115],"period":[116,166,206],"incrementing":[117,167,211],"structures":[118],"can":[119],"be":[120],"observed,":[121],"where":[122],"boundaries":[124],"periodicity":[127],"region":[128],"are":[129,179,194,207],"either":[131],"subcritical,":[133,180],"or":[134,136,150],"supercritical,":[135],"degenerate":[137],"flip":[138,177,192],"bifurcations":[139,178,193],"cycle,":[143],"as":[144,146],"well":[145],"BCB.":[152],"In":[153],"particular,":[154],"positive":[159],"smaller":[161],"than":[162,187],"one,":[163,188],"bistability":[170],"regions":[171,200],"observed":[173],"corresponding":[176],"larger":[186],"supercritical":[195],"and,":[196],"thus,":[197],"also":[198],"associated":[201],"cycles":[203],"double":[205],"involved":[208],"into":[209],"structure.":[212]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
