{"id":"https://openalex.org/W3157084458","doi":"https://doi.org/10.1142/s0218127421300159","title":"Phenomena of Bifurcation and Chaos in the Dynamically Loaded Hyperelastic Spherical Membrane Based on a Noninteger Power-Law Constitutive Model","display_name":"Phenomena of Bifurcation and Chaos in the Dynamically Loaded Hyperelastic Spherical Membrane Based on a Noninteger Power-Law Constitutive Model","publication_year":2021,"publication_date":"2021-04-01","ids":{"openalex":"https://openalex.org/W3157084458","doi":"https://doi.org/10.1142/s0218127421300159","mag":"3157084458"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127421300159","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421300159","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/A5089742915","display_name":"Zhentao Zhao","orcid":"https://orcid.org/0000-0003-0513-860X"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhentao Zhao","raw_affiliation_strings":["State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, P. R. China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024401516","display_name":"Xuegang Yuan","orcid":"https://orcid.org/0000-0003-4719-364X"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]},{"id":"https://openalex.org/I61565387","display_name":"Dalian Minzu University","ror":"https://ror.org/02hxfx521","country_code":"CN","type":"education","lineage":["https://openalex.org/I61565387"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuegang Yuan","raw_affiliation_strings":["School of Science, Dalian Minzu University, Dalian 116600, P. R. China","State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-4719-364X","affiliations":[{"raw_affiliation_string":"School of Science, Dalian Minzu University, Dalian 116600, P. R. China","institution_ids":["https://openalex.org/I61565387"]},{"raw_affiliation_string":"State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, P. R. China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008984643","display_name":"Datian Niu","orcid":"https://orcid.org/0009-0004-5817-6540"},"institutions":[{"id":"https://openalex.org/I61565387","display_name":"Dalian Minzu University","ror":"https://ror.org/02hxfx521","country_code":"CN","type":"education","lineage":["https://openalex.org/I61565387"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Datian Niu","raw_affiliation_strings":["School of Science, Dalian Minzu University, Dalian 116600, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Dalian Minzu University, Dalian 116600, P. R. China","institution_ids":["https://openalex.org/I61565387"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100611736","display_name":"Wenzheng Zhang","orcid":"https://orcid.org/0000-0001-9012-0396"},"institutions":[{"id":"https://openalex.org/I61565387","display_name":"Dalian Minzu University","ror":"https://ror.org/02hxfx521","country_code":"CN","type":"education","lineage":["https://openalex.org/I61565387"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenzheng Zhang","raw_affiliation_strings":["School of Science, Dalian Minzu University, Dalian 116600, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Dalian Minzu University, Dalian 116600, P. R. China","institution_ids":["https://openalex.org/I61565387"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103815552","display_name":"Hongwu Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongwu Zhang","raw_affiliation_strings":["State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, P. R. China","institution_ids":["https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2547,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.48801792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"31","issue":"05","first_page":"2130015","last_page":"2130015"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13261","display_name":"Elasticity and Wave Propagation","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7667937278747559},{"id":"https://openalex.org/keywords/hyperelastic-material","display_name":"Hyperelastic material","score":0.7204347252845764},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6124988794326782},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5910134315490723},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5495103001594543},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5437697768211365},{"id":"https://openalex.org/keywords/power-law","display_name":"Power law","score":0.5297775268554688},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.488739013671875},{"id":"https://openalex.org/keywords/constitutive-equation","display_name":"Constitutive equation","score":0.4614608883857727},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.44088250398635864},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.4198802411556244},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.35224878787994385},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3125923275947571},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2513427138328552},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08193376660346985},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.0689471960067749}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7667937278747559},{"id":"https://openalex.org/C147370603","wikidata":"https://www.wikidata.org/wiki/Q3801506","display_name":"Hyperelastic material","level":3,"score":0.7204347252845764},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6124988794326782},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5910134315490723},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5495103001594543},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5437697768211365},{"id":"https://openalex.org/C87040749","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Power law","level":2,"score":0.5297775268554688},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.488739013671875},{"id":"https://openalex.org/C202973686","wikidata":"https://www.wikidata.org/wiki/Q1937401","display_name":"Constitutive equation","level":3,"score":0.4614608883857727},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.44088250398635864},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.4198802411556244},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.35224878787994385},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3125923275947571},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2513427138328552},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08193376660346985},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0689471960067749},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127421300159","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421300159","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":[{"display_name":"Peace, Justice and strong institutions","score":0.44999998807907104,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G2338968032","display_name":null,"funder_award_id":"11872145","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G609945486","display_name":null,"funder_award_id":"11672062","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8582422557","display_name":null,"funder_award_id":"11672069","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8865327836","display_name":null,"funder_award_id":"11702059","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W228745176","https://openalex.org/W1184165589","https://openalex.org/W1966259987","https://openalex.org/W1969279651","https://openalex.org/W1980508917","https://openalex.org/W1988551837","https://openalex.org/W1989339109","https://openalex.org/W1994460844","https://openalex.org/W1997436998","https://openalex.org/W1998988417","https://openalex.org/W2006730584","https://openalex.org/W2009937137","https://openalex.org/W2027828326","https://openalex.org/W2032458303","https://openalex.org/W2038995371","https://openalex.org/W2043428911","https://openalex.org/W2048090284","https://openalex.org/W2081892702","https://openalex.org/W2083899872","https://openalex.org/W2085064593","https://openalex.org/W2113646525","https://openalex.org/W2124428761","https://openalex.org/W2152254020","https://openalex.org/W2163592686","https://openalex.org/W2178147694","https://openalex.org/W2259013286","https://openalex.org/W2566671756","https://openalex.org/W2567423323","https://openalex.org/W2605543710","https://openalex.org/W2745041239","https://openalex.org/W2770509250","https://openalex.org/W2884400302","https://openalex.org/W2914202534","https://openalex.org/W2956117974","https://openalex.org/W2970763903","https://openalex.org/W2974280364","https://openalex.org/W3005545283","https://openalex.org/W3011843610","https://openalex.org/W3027073189","https://openalex.org/W3031022984"],"related_works":["https://openalex.org/W2106448822","https://openalex.org/W2546487931","https://openalex.org/W3145971316","https://openalex.org/W2319243846","https://openalex.org/W1194905386","https://openalex.org/W2159151868","https://openalex.org/W2019539136","https://openalex.org/W4245057904","https://openalex.org/W4226340181","https://openalex.org/W1986286210"],"abstract_inverted_index":{"The":[0],"phenomena":[1],"of":[2,11,29,37,71,81,84,100,108],"bifurcation":[3,98],"and":[4,105,120,130],"chaos":[5],"are":[6,74,103,111,123],"studied":[7],"for":[8,88,113,125],"a":[9,43,89,114],"class":[10],"second":[12],"order":[13],"nonlinear":[14,25],"nonautonomous":[15],"ordinary":[16],"differential":[17],"equations,":[18],"which":[19],"may":[20],"be":[21],"formulated":[22],"by":[23],"the":[24,30,38,50,53,57,62,68,72,93,97,106,118,126],"radially":[26],"symmetric":[27,64],"motion":[28],"dynamically":[31],"loaded":[32],"hyperelastic":[33],"spherical":[34],"membrane":[35],"composed":[36],"Rivlin\u2013Saunders":[39],"material":[40,85],"model":[41],"with":[42,61,128],"noninteger":[44],"power-law":[45],"exponent.":[46],"Firstly,":[47],"based":[48],"on":[49],"variational":[51],"principle,":[52],"governing":[54],"equation":[55],"describing":[56,96],"problem":[58],"is":[59],"obtained":[60],"spherically":[63],"deformation":[65],"assumption.":[66],"Then,":[67],"dynamic":[69],"characteristics":[70,107],"system":[73],"qualitatively":[75],"analyzed":[76],"in":[77,79],"detail":[78],"terms":[80],"different":[82],"values":[83],"parameters.":[86],"Particularly,":[87],"given":[90],"constant":[91],"load,":[92,117],"parameter":[94],"spaces":[95],"behaviors":[99,122],"equilibrium":[101,109,132],"curves":[102],"established":[104],"points":[110],"presented;":[112],"periodically":[115],"perturbed":[116],"quasi-periodic":[119],"chaotic":[121],"discussed":[124],"systems":[127],"two":[129],"three":[131],"points,":[133],"respectively.":[134]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
