{"id":"https://openalex.org/W4406938660","doi":"https://doi.org/10.1142/s0218127425500245","title":"Li\u2013Yorke Chaos in Partial Differential Equations with or Without Energy Injection","display_name":"Li\u2013Yorke Chaos in Partial Differential Equations with or Without Energy Injection","publication_year":2025,"publication_date":"2025-01-29","ids":{"openalex":"https://openalex.org/W4406938660","doi":"https://doi.org/10.1142/s0218127425500245"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127425500245","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425500245","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/A5100437233","display_name":"Xu Zhang","orcid":"https://orcid.org/0000-0002-5138-6631"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xu Zhang","raw_affiliation_strings":["Department of Mathematics, Shandong University, Weihai 264209, Shandong, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-5138-6631","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shandong University, Weihai 264209, Shandong, P. R. China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114646441","display_name":"Iram Hussan","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Iram Hussan","raw_affiliation_strings":["Department of Mathematics, Shandong University, Weihai 264209, Shandong, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shandong University, Weihai 264209, Shandong, P. R. China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012287783","display_name":"Manyu Zhao","orcid":"https://orcid.org/0009-0005-4362-239X"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Manyu Zhao","raw_affiliation_strings":["Department of Mathematics, Shandong University, Weihai 264209, Shandong, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shandong University, Weihai 264209, Shandong, P. R. China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080858709","display_name":"Qigui Yang","orcid":"https://orcid.org/0000-0002-3623-4947"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qigui Yang","raw_affiliation_strings":["School of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, P. R. China","institution_ids":["https://openalex.org/I90610280"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100437233"],"corresponding_institution_ids":["https://openalex.org/I154099455"],"apc_list":null,"apc_paid":null,"fwci":1.1805,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.75685402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"35","issue":"02","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9218000173568726,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9218000173568726,"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/chaos","display_name":"CHAOS (operating system)","score":0.7080992460250854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5602016448974609},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4882779121398926},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4701170027256012},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.45635417103767395},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.43627044558525085},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.41722673177719116},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39231637120246887},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.313914954662323},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2757991552352905},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.15807440876960754},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.11877521872520447},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09419283270835876},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09068378806114197}],"concepts":[{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.7080992460250854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5602016448974609},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4882779121398926},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4701170027256012},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.45635417103767395},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.43627044558525085},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.41722673177719116},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39231637120246887},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.313914954662323},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2757991552352905},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.15807440876960754},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.11877521872520447},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09419283270835876},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09068378806114197},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127425500245","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425500245","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":[{"id":"https://openalex.org/G212970494","display_name":null,"funder_award_id":"12471160","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3189564351","display_name":null,"funder_award_id":"2024A1515011425","funder_id":"https://openalex.org/F4320337111","funder_display_name":"Basic and Applied Basic Research Foundation of Guangdong Province"},{"id":"https://openalex.org/G8503797174","display_name":null,"funder_award_id":"ZR2023MA047","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null},{"id":"https://openalex.org/F4320337111","display_name":"Basic and Applied Basic Research Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W85931118","https://openalex.org/W1641808155","https://openalex.org/W1855169650","https://openalex.org/W1961956412","https://openalex.org/W1967829438","https://openalex.org/W1970234221","https://openalex.org/W1977483907","https://openalex.org/W1980581130","https://openalex.org/W1985940938","https://openalex.org/W2006553622","https://openalex.org/W2016021508","https://openalex.org/W2025880370","https://openalex.org/W2039389503","https://openalex.org/W2046402307","https://openalex.org/W2050210602","https://openalex.org/W2052686002","https://openalex.org/W2054604235","https://openalex.org/W2059793594","https://openalex.org/W2061191702","https://openalex.org/W2063903387","https://openalex.org/W2067503923","https://openalex.org/W2069172908","https://openalex.org/W2069356133","https://openalex.org/W2075137857","https://openalex.org/W2080197786","https://openalex.org/W2080858310","https://openalex.org/W2095194040","https://openalex.org/W2141394518","https://openalex.org/W2277514911","https://openalex.org/W2320810720","https://openalex.org/W2322149312","https://openalex.org/W2602676502","https://openalex.org/W2766703771","https://openalex.org/W2792586619","https://openalex.org/W2792957628","https://openalex.org/W2798260098","https://openalex.org/W2903097570","https://openalex.org/W2963448313","https://openalex.org/W3005628918","https://openalex.org/W3082795004","https://openalex.org/W3105843439","https://openalex.org/W3168588740","https://openalex.org/W4210970305","https://openalex.org/W4220732723","https://openalex.org/W4221036531","https://openalex.org/W4229951232","https://openalex.org/W4241440483","https://openalex.org/W4256081943","https://openalex.org/W4285206069","https://openalex.org/W4292024663","https://openalex.org/W4294738854","https://openalex.org/W4298374011","https://openalex.org/W4312587821"],"related_works":["https://openalex.org/W2320196587","https://openalex.org/W4400519012","https://openalex.org/W4243901518","https://openalex.org/W4383267773","https://openalex.org/W3110439525","https://openalex.org/W4251075027","https://openalex.org/W2393451533","https://openalex.org/W2358131398","https://openalex.org/W2027932829","https://openalex.org/W128153361"],"abstract_inverted_index":{"Many":[0],"physical":[1,144],"systems":[2,18,45],"are":[3,61,97],"represented":[4],"by":[5],"Partial":[6],"Differential":[7],"Equations":[8],"(PDEs),":[9],"and":[10,21,33,80,115],"the":[11,26,34,52,64,87,106,132,135],"study":[12],"of":[13,29,42,59,66,72,77,83,95,102,105,112,118,134,138,158],"chaotic":[14],"dynamics":[15,137],"in":[16,39,148],"these":[17,139],"is":[19,31,37,123,128,151],"interesting":[20,156],"challenging.":[22],"In":[23,141],"this":[24],"paper,":[25],"Li\u2013Yorke":[27,35,67,126],"chaos":[28,36,127,147],"PDEs":[30,53,60,88,96,150],"studied,":[32,98],"observable":[38],"several":[40],"classes":[41],"PDEs,":[43],"including":[44,69,99],"with":[46,89,108],"or":[47],"without":[48,54],"energy":[49,55,90],"injection.":[50],"For":[51,86],"injection,":[56,91],"three":[57],"kinds":[58],"investigated":[62],"revealing":[63],"existence":[65],"chaos,":[68],"a":[70,75,81,100,110,116,143],"type":[71,94],"transport":[73],"equations,":[74,79,114],"class":[76,117],"wave":[78],"kind":[82,111],"Navier\u2013Stokes":[84,120],"equations.":[85,121],"only":[92],"dissipative":[93],"model":[101],"sound":[103],"variation":[104],"drum":[107],"damping,":[109],"reaction\u2013diffusion":[113],"two-dimensional":[119],"It":[122],"shown":[124],"that":[125],"well":[129],"defined":[130],"for":[131],"characterization":[133],"complicated":[136],"systems.":[140],"particular,":[142],"explanation":[145,157],"about":[146],"such":[149],"provided,":[152],"which":[153],"gives":[154],"an":[155],"acoustic":[159],"chaos.":[160]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}