{"id":"https://openalex.org/W2764326189","doi":"https://doi.org/10.1142/s0218127417300324","title":"On the Inverse Problem of Competitive Modes and the Search for Chaotic Dynamics","display_name":"On the Inverse Problem of Competitive Modes and the Search for Chaotic Dynamics","publication_year":2017,"publication_date":"2017-09-01","ids":{"openalex":"https://openalex.org/W2764326189","doi":"https://doi.org/10.1142/s0218127417300324","mag":"2764326189"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127417300324","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417300324","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/A5069325215","display_name":"Lewis Ruks","orcid":"https://orcid.org/0000-0002-5593-3233"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Lewis Ruks","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056297542","display_name":"Robert A. Van Gorder","orcid":"https://orcid.org/0000-0002-8506-3961"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Robert A. Van Gorder","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069325215"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":0.6919,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.69837647,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"27","issue":"10","first_page":"1730032","last_page":"1730032"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9980999827384949,"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/T10244","display_name":"Chaos control and synchronization","score":0.9980999827384949,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9943000078201294,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9886999726295471,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.7159533500671387},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6357325315475464},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5834288597106934},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5525840520858765},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5423039793968201},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.512696385383606},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.478975772857666},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45281898975372314},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44671934843063354},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3413239121437073},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30695152282714844},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09384974837303162}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.7159533500671387},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6357325315475464},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5834288597106934},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5525840520858765},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5423039793968201},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.512696385383606},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.478975772857666},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45281898975372314},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44671934843063354},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3413239121437073},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30695152282714844},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09384974837303162},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127417300324","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417300324","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.ox.ac.uk:uuid:7dffe05a-ed8a-4810-a25c-ca63b41b98fb","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:7dffe05a-ed8a-4810-a25c-ca63b41b98fb","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1521738998","https://openalex.org/W1526758300","https://openalex.org/W1680579736","https://openalex.org/W1964873435","https://openalex.org/W1965360919","https://openalex.org/W1967008192","https://openalex.org/W1970650503","https://openalex.org/W1979684610","https://openalex.org/W1981528870","https://openalex.org/W1993183384","https://openalex.org/W1993675804","https://openalex.org/W2015317142","https://openalex.org/W2031668778","https://openalex.org/W2032217612","https://openalex.org/W2034557530","https://openalex.org/W2044383346","https://openalex.org/W2046017935","https://openalex.org/W2069436097","https://openalex.org/W2076374097","https://openalex.org/W2076962667","https://openalex.org/W2082633491","https://openalex.org/W2089876099","https://openalex.org/W2092360752","https://openalex.org/W2111939941","https://openalex.org/W2135128351","https://openalex.org/W2141394518","https://openalex.org/W2152254020","https://openalex.org/W2155445353","https://openalex.org/W2168519697","https://openalex.org/W2205318720","https://openalex.org/W2315759974","https://openalex.org/W2408502140","https://openalex.org/W2497296206","https://openalex.org/W2554114274","https://openalex.org/W2580204640","https://openalex.org/W2598617614"],"related_works":["https://openalex.org/W2230606337","https://openalex.org/W4250831671","https://openalex.org/W2089869689","https://openalex.org/W4388681848","https://openalex.org/W2078952919","https://openalex.org/W2945666329","https://openalex.org/W2617651062","https://openalex.org/W2377513064","https://openalex.org/W2016990342","https://openalex.org/W2952544653"],"abstract_inverted_index":{"Generalized":[0],"competitive":[1,189],"modes":[2,57,160],"(GCM)":[3],"have":[4],"been":[5],"used":[6],"as":[7,40],"a":[8,25,41,76,91,172,219],"diagnostic":[9],"tool":[10],"in":[11,24,209],"order":[12,28,38,43,80,93,210],"to":[13,21,50,109,112,126,153,183,201,211],"analytically":[14],"identify":[15],"parameter":[16],"regimes":[17,171,180],"which":[18,98],"may":[19],"lead":[20,182],"chaotic":[22,100,170,240],"trajectories":[23],"given":[26],"first":[27,37,92],"nonlinear":[29,44,147],"dynamical":[30,94,196],"system.":[31],"The":[32],"approach":[33,221],"involves":[34],"recasting":[35],"the":[36,56,64,70,84,103,117,133,146,159,188,203],"system":[39,77,95],"second":[42,79],"oscillator":[45,81],"system,":[46,129],"and":[47,192,227],"then":[48,89,198],"checking":[49],"see":[51],"if":[52],"certain":[53],"conditions":[54],"on":[55],"of":[58,73,78,116,138,158,178,195],"these":[59,165],"oscillators":[60],"are":[61,122,151,185,230],"satisfied.":[62],"In":[63],"present":[65],"paper,":[66],"we":[67,88,130,150],"will":[68],"consider":[69,132],"inverse":[71,105],"problem":[72,106,134],"GCM:":[74],"If":[75],"equations":[82],"satisfy":[83],"GCM":[85],"conditions,":[86,191],"can":[87],"construct":[90],"from":[96],"it":[97],"admits":[99],"trajectories?":[101],"Solving":[102],"direct":[104],"is":[107,222],"equivalent":[108],"finding":[110,169],"solutions":[111,125],"an":[113],"inhomogeneous":[114],"form":[115],"Euler":[118],"equations.":[119],"As":[120],"there":[121],"no":[123],"general":[124],"this":[127],"PDE":[128],"instead":[131],"for":[135,140,237],"restricted":[136],"classes":[137,177],"functions":[139,207],"autonomous":[141],"systems":[142,197],"which,":[143],"upon":[144],"obtaining":[145],"oscillatory":[148],"representation,":[149],"able":[152],"extract":[154],"at":[155],"least":[156],"two":[157],"explicitly.":[161],"We":[162],"find":[163,215],"that":[164,181],"methods":[166],"often":[167],"make":[168],"much":[173],"simpler":[174],"task;":[175],"many":[176],"parameter-function":[179],"nonchaos":[184],"excluded":[186],"by":[187],"mode":[190],"classical":[193],"knowledge":[194],"allows":[199],"us":[200],"tune":[202],"free":[204],"parameters":[205],"or":[206,241],"appropriately":[208],"obtain":[212],"chaos.":[213],"To":[214],"new":[216,239],"hyperchaotic":[217,242],"systems,":[218],"similar":[220],"used,":[223],"but":[224],"more":[225],"effort":[226],"additional":[228],"considerations":[229],"needed.":[231],"These":[232],"results":[233],"demonstrate":[234],"one":[235],"method":[236],"constructing":[238],"systems.":[243]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
