{"id":"https://openalex.org/W4388105064","doi":"https://doi.org/10.1142/s0218127423300331","title":"Spikes Adding to Infinity on Period-1 Orbits to Chaos in the R\u00f6ssler System","display_name":"Spikes Adding to Infinity on Period-1 Orbits to Chaos in the R\u00f6ssler System","publication_year":2023,"publication_date":"2023-10-01","ids":{"openalex":"https://openalex.org/W4388105064","doi":"https://doi.org/10.1142/s0218127423300331"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127423300331","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423300331","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/A5003255279","display_name":"Siyuan Xing","orcid":"https://orcid.org/0000-0001-6916-719X"},"institutions":[{"id":"https://openalex.org/I149919469","display_name":"California Polytechnic State University","ror":"https://ror.org/001gpfp45","country_code":"US","type":"education","lineage":["https://openalex.org/I149919469"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Siyuan Xing","raw_affiliation_strings":["Department of Mechanical Engineering, California Polytechnic State University, San Luis Obispo, CA 93407, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, California Polytechnic State University, San Luis Obispo, CA 93407, USA","institution_ids":["https://openalex.org/I149919469"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076270155","display_name":"Albert C. J. Luo","orcid":"https://orcid.org/0000-0001-8208-6108"},"institutions":[{"id":"https://openalex.org/I87547150","display_name":"Southern Illinois University Edwardsville","ror":"https://ror.org/04cqs5j56","country_code":"US","type":"education","lineage":["https://openalex.org/I2801502357","https://openalex.org/I87547150"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Albert C. J. Luo","raw_affiliation_strings":["Department of Mechanical and Mechatronics Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA"],"raw_orcid":"https://orcid.org/0000-0001-8208-6108","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Mechatronics Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA","institution_ids":["https://openalex.org/I87547150"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076270155"],"corresponding_institution_ids":["https://openalex.org/I87547150"],"apc_list":null,"apc_paid":null,"fwci":0.9604,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.77449146,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"33","issue":"13","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9993000030517578,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.996399998664856,"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/period","display_name":"Period (music)","score":0.7961921691894531},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.6682462692260742},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6315670013427734},{"id":"https://openalex.org/keywords/heteroclinic-orbit","display_name":"Heteroclinic orbit","score":0.5145149230957031},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.4914132356643677},{"id":"https://openalex.org/keywords/period-length","display_name":"Period length","score":0.48724403977394104},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.48122596740722656},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.46766984462738037},{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.4662408232688904},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.415093332529068},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3302386999130249},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.2749456763267517},{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.1758752465248108},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.14478924870491028},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09192106127738953},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08436241745948792}],"concepts":[{"id":"https://openalex.org/C2781291010","wikidata":"https://www.wikidata.org/wiki/Q178580","display_name":"Period (music)","level":2,"score":0.7961921691894531},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.6682462692260742},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6315670013427734},{"id":"https://openalex.org/C184481792","wikidata":"https://www.wikidata.org/wiki/Q1992087","display_name":"Heteroclinic orbit","level":5,"score":0.5145149230957031},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.4914132356643677},{"id":"https://openalex.org/C2910820772","wikidata":"https://www.wikidata.org/wiki/Q184743","display_name":"Period length","level":2,"score":0.48724403977394104},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.48122596740722656},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.46766984462738037},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.4662408232688904},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.415093332529068},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3302386999130249},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.2749456763267517},{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.1758752465248108},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.14478924870491028},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09192106127738953},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08436241745948792},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127423300331","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423300331","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1964818691","https://openalex.org/W1967008192","https://openalex.org/W1968220940","https://openalex.org/W1997509966","https://openalex.org/W2028679871","https://openalex.org/W2050552960","https://openalex.org/W2056242511","https://openalex.org/W2069765806","https://openalex.org/W2085988745","https://openalex.org/W2091314510","https://openalex.org/W2094871671","https://openalex.org/W2119368478","https://openalex.org/W2168856305","https://openalex.org/W2275890290","https://openalex.org/W2484139121","https://openalex.org/W2989276764","https://openalex.org/W3103487715","https://openalex.org/W3148615883","https://openalex.org/W3196039654","https://openalex.org/W4213302443","https://openalex.org/W4226247819","https://openalex.org/W4231871155","https://openalex.org/W4283077946","https://openalex.org/W4310927679","https://openalex.org/W4361000480"],"related_works":["https://openalex.org/W1999123830","https://openalex.org/W2072009444","https://openalex.org/W2081334888","https://openalex.org/W3151500797","https://openalex.org/W2024454600","https://openalex.org/W3142626835","https://openalex.org/W3145975296","https://openalex.org/W2015099410","https://openalex.org/W2085868801","https://openalex.org/W2350473807"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"spikes":[3,22,164,170,176],"adding":[4,23,171,177],"to":[5,13,54,61,68,108,120,138,159,184],"infinity":[6],"on":[7,24,43,92,172],"bifurcation":[8,75,126],"trees":[9,127],"of":[10,36,76,128,153,169,181],"period-1":[11,38,46,60,78,95,99,107,129,158,182],"orbits":[12,27,65,112,130,140,161,183],"chaos":[14,185],"in":[15],"the":[16,25,50,59,98,179],"R\u00f6ssler":[17],"system":[18],"is":[19,28,41,90],"studied.":[20],"The":[21,124,148,175],"periodic":[26,173],"completed":[29],"through":[30],"a":[31,37,45,73,77,87,94,106],"saddle-node":[32],"bifurcation.":[33],"With":[34],"onset":[35],"orbit,":[39,47],"there":[40],"1-spike":[42,53,67],"such":[44,93],"followed":[48],"by":[49],"development":[51],"from":[52],"[Formula:":[55,69,81,102,117,121,132,142,154],"see":[56,63,70,82,85,103,110,114,118,122,133,136,143,155],"text]-spikes":[57,83,119,134,144],"and":[58,151],"period-[Formula:":[62,109],"text]":[64,111],"have":[66,116],"text]-spikes.":[71,104,123],"For":[72],"spike":[74,89],"orbit":[79,100],"with":[80,131,141,162],"([Formula:":[84,113,135],"text]),":[86],"new":[88],"added":[91],"orbit.":[96],"Thus,":[97],"has":[101],"Such":[105],"text])":[115,137],"three":[125],"period-4":[139,160],"are":[145,165],"presented":[146],"numerically.":[147],"phase":[149],"trajectories":[150],"responses":[152],"text]-component":[156],"for":[157,167],"different":[163],"given":[166],"illustrations":[168],"orbits.":[174],"generating":[178],"complexity":[180],"can":[186],"be":[187],"developed.":[188]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}