{"id":"https://openalex.org/W2730429383","doi":"https://doi.org/10.1142/s0218127417300221","title":"On Discontinuous Piecewise Linear Models for Memristor Oscillators","display_name":"On Discontinuous Piecewise Linear Models for Memristor Oscillators","publication_year":2017,"publication_date":"2017-06-15","ids":{"openalex":"https://openalex.org/W2730429383","doi":"https://doi.org/10.1142/s0218127417300221","mag":"2730429383"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127417300221","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417300221","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/A5091250943","display_name":"Andr\u00e9s Amador","orcid":"https://orcid.org/0000-0001-9525-4289"},"institutions":[{"id":"https://openalex.org/I233745408","display_name":"Pontificia Universidad Javeriana","ror":"https://ror.org/03etyjw28","country_code":"CO","type":"education","lineage":["https://openalex.org/I233745408"]}],"countries":["CO"],"is_corresponding":true,"raw_author_name":"Andr\u00e9s Amador","raw_affiliation_strings":["Departamento de Ciencias Naturales y Matem\u00e1ticas, Pontificia Universidad Javeriana-Cali, Calle 18, No. 118-250, Santiago de Cali, Colombia"],"affiliations":[{"raw_affiliation_string":"Departamento de Ciencias Naturales y Matem\u00e1ticas, Pontificia Universidad Javeriana-Cali, Calle 18, No. 118-250, Santiago de Cali, Colombia","institution_ids":["https://openalex.org/I233745408"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079661353","display_name":"E. Freire","orcid":"https://orcid.org/0000-0001-5852-0699"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Emilio Freire","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada II, Universidad de Sevilla, Escuela T\u00e9cnica Superior de Ingenier\u00eda, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada II, Universidad de Sevilla, Escuela T\u00e9cnica Superior de Ingenier\u00eda, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020350489","display_name":"Enrique Ponce","orcid":"https://orcid.org/0000-0003-0467-5032"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Enrique Ponce","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada II, Universidad de Sevilla, Escuela T\u00e9cnica Superior de Ingenier\u00eda, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada II, Universidad de Sevilla, Escuela T\u00e9cnica Superior de Ingenier\u00eda, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073952420","display_name":"Javier Ros","orcid":"https://orcid.org/0000-0002-6396-1461"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Javier Ros","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada II, Universidad de Sevilla, Escuela T\u00e9cnica Superior de Ingenier\u00eda, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada II, Universidad de Sevilla, Escuela T\u00e9cnica Superior de Ingenier\u00eda, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5091250943"],"corresponding_institution_ids":["https://openalex.org/I233745408"],"apc_list":null,"apc_paid":null,"fwci":1.6576,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.86138351,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"27","issue":"06","first_page":"1730022","last_page":"1730022"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9993000030517578,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9993000030517578,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9987999796867371,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9976000189781189,"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/memristor","display_name":"Memristor","score":0.8561031818389893},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6818503141403198},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.6287349462509155},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.601356029510498},{"id":"https://openalex.org/keywords/bistability","display_name":"Bistability","score":0.5990009903907776},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5952644348144531},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5487977266311646},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.5310357809066772},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5081350803375244},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5072307586669922},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.48665672540664673},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4759376049041748},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4427788555622101},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.43809840083122253},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.42557844519615173},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3318334221839905},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2851617932319641},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15815696120262146},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14268752932548523},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09647771716117859},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.07567673921585083}],"concepts":[{"id":"https://openalex.org/C150072547","wikidata":"https://www.wikidata.org/wiki/Q212923","display_name":"Memristor","level":2,"score":0.8561031818389893},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6818503141403198},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.6287349462509155},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.601356029510498},{"id":"https://openalex.org/C97292510","wikidata":"https://www.wikidata.org/wiki/Q2304620","display_name":"Bistability","level":2,"score":0.5990009903907776},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5952644348144531},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5487977266311646},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.5310357809066772},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5081350803375244},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5072307586669922},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.48665672540664673},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4759376049041748},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4427788555622101},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.43809840083122253},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.42557844519615173},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3318334221839905},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2851617932319641},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15815696120262146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14268752932548523},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09647771716117859},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.07567673921585083},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127417300221","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417300221","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":[{"score":0.4300000071525574,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320325859","display_name":"Pontificia Universidad Javeriana","ror":"https://ror.org/03etyjw28"},{"id":"https://openalex.org/F4320326754","display_name":"Junta de Andaluc\u00eda","ror":"https://ror.org/01jem9c82"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1602558726","https://openalex.org/W1993214330","https://openalex.org/W2005800326","https://openalex.org/W2018888755","https://openalex.org/W2033148498","https://openalex.org/W2044805414","https://openalex.org/W2047449028","https://openalex.org/W2064455533","https://openalex.org/W2088070114","https://openalex.org/W2088972854","https://openalex.org/W2099179260","https://openalex.org/W2102216069","https://openalex.org/W2112181056","https://openalex.org/W2162651880","https://openalex.org/W2188902357","https://openalex.org/W2485899172","https://openalex.org/W2510211160","https://openalex.org/W2562841853","https://openalex.org/W3102137675","https://openalex.org/W4247151931"],"related_works":["https://openalex.org/W4229452466","https://openalex.org/W2966276069","https://openalex.org/W4224217224","https://openalex.org/W2548107569","https://openalex.org/W2088727788","https://openalex.org/W44694169","https://openalex.org/W1674348501","https://openalex.org/W1971277302","https://openalex.org/W1964489467","https://openalex.org/W2030497467"],"abstract_inverted_index":{"In":[0,21],"this":[1],"paper,":[2],"we":[3,33],"provide":[4],"for":[5,23,99],"the":[6,13,35,46,77,85,111,133,139,156],"first":[7],"time":[8],"rigorous":[9],"mathematical":[10],"results":[11,98,113],"regarding":[12],"rich":[14],"dynamics":[15,47],"of":[16,37,41,96,135,151,159,170,177],"piecewise":[17,102],"linear":[18,103],"memristor":[19,91],"oscillators.":[20],"particular,":[22],"each":[24],"nonlinear":[25],"oscillator":[26],"given":[27],"in":[28,115,138],"[Itoh":[29],"&":[30,123],"Chua,":[31],"2008],":[32],"show":[34],"existence":[36,134],"an":[38],"infinite":[39,157],"family":[40],"invariant":[42],"manifolds":[43,50],"and":[44],"that":[45,154],"on":[48],"such":[49],"can":[51],"be":[52],"modeled":[53],"without":[54],"resorting":[55],"to":[56,76,83],"discontinuous":[57],"models.":[58],"Our":[59],"approach":[60],"provides":[61],"topologically":[62],"equivalent":[63],"continuous":[64,101],"models":[65],"with":[66,71],"one":[67,72],"dimension":[68],"less":[69],"but":[70,126],"extra":[73],"parameter":[74],"associated":[75],"initial":[78,152],"conditions.":[79],"It":[80],"is":[81,166,179],"possible":[82],"justify":[84,155],"periodic":[86,146,160],"behavior":[87],"exhibited":[88,162],"by":[89,93,131,145,163],"three-dimensional":[90],"oscillators,":[92],"taking":[94],"advantage":[95],"known":[97],"planar":[100],"systems.":[104],"The":[105,148,168],"analysis":[106],"developed":[107],"not":[108],"only":[109],"confirms":[110],"numerical":[112],"contained":[114],"previous":[116],"works":[117],"[Messias":[118],"et":[119],"al.,":[120],"2010;":[121],"Scarabello":[122],"Messias,":[124],"2014]":[125],"also":[127,180],"goes":[128],"much":[129],"further":[130],"showing":[132],"closed":[136],"surfaces":[137],"state":[140],"space":[141],"which":[142],"are":[143],"foliated":[144],"orbits.":[147],"important":[149],"role":[150],"conditions":[153],"number":[158],"orbits":[161],"these":[164],"models,":[165],"stressed.":[167],"possibility":[169],"unsuspected":[171],"bistable":[172],"regimes":[173],"under":[174],"specific":[175],"configurations":[176],"parameters":[178],"emphasized.":[181]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}