{"id":"https://openalex.org/W2004613851","doi":"https://doi.org/10.1109/icca.2014.6870914","title":"The distance-to-bifurcation problem in non-negative dynamical systems with kinetic realizations","display_name":"The distance-to-bifurcation problem in non-negative dynamical systems with kinetic realizations","publication_year":2014,"publication_date":"2014-06-01","ids":{"openalex":"https://openalex.org/W2004613851","doi":"https://doi.org/10.1109/icca.2014.6870914","mag":"2004613851"},"language":"en","primary_location":{"id":"doi:10.1109/icca.2014.6870914","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icca.2014.6870914","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"11th IEEE International Conference on Control &amp; Automation (ICCA)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5025702566","display_name":"Tua A. Tamba","orcid":"https://orcid.org/0000-0003-4702-1100"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tua A. Tamba","raw_affiliation_strings":["Department of Electrical Engineering, University of Notre Dame, USA","[Dept. of Electr. Eng., Univ. of Notre Dame, Notre Dame, IN, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Notre Dame, USA","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"[Dept. of Electr. Eng., Univ. of Notre Dame, Notre Dame, IN, USA]","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022295836","display_name":"Michael Lemmon","orcid":null},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M.D. Lemmon","raw_affiliation_strings":["Department of Electrical Engineering, University of Notre Dame, USA","[Dept. of Electr. Eng., Univ. of Notre Dame, Notre Dame, IN, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Notre Dame, USA","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"[Dept. of Electr. Eng., Univ. of Notre Dame, Notre Dame, IN, USA]","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I107639228"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"212","issue":null,"first_page":"162","last_page":"167"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T13539","display_name":"thermodynamics and calorimetric analyses","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/1606","display_name":"Physical and Theoretical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10932","display_name":"Microbial Metabolic Engineering and Bioproduction","score":0.9811000227928162,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.6543543934822083},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6079925298690796},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5836191773414612},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.45314085483551025},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45142096281051636},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4214699864387512},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4106408953666687},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3785327076911926},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37559643387794495},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36866939067840576},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33540868759155273},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15061265230178833},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07532200217247009}],"concepts":[{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.6543543934822083},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6079925298690796},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5836191773414612},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.45314085483551025},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45142096281051636},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4214699864387512},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4106408953666687},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3785327076911926},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37559643387794495},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36866939067840576},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33540868759155273},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15061265230178833},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07532200217247009},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icca.2014.6870914","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icca.2014.6870914","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"11th IEEE International Conference on Control &amp; Automation (ICCA)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/2","score":0.5299999713897705,"display_name":"Zero hunger"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W615876487","https://openalex.org/W1496146011","https://openalex.org/W1539838732","https://openalex.org/W1596321532","https://openalex.org/W1967073510","https://openalex.org/W1967184028","https://openalex.org/W1970573500","https://openalex.org/W1987811288","https://openalex.org/W1988507461","https://openalex.org/W2004746351","https://openalex.org/W2017483928","https://openalex.org/W2020554592","https://openalex.org/W2022666585","https://openalex.org/W2023484826","https://openalex.org/W2028773706","https://openalex.org/W2033414977","https://openalex.org/W2034787898","https://openalex.org/W2038388741","https://openalex.org/W2039325506","https://openalex.org/W2045020702","https://openalex.org/W2045275095","https://openalex.org/W2057467365","https://openalex.org/W2061038733","https://openalex.org/W2075273870","https://openalex.org/W2085352155","https://openalex.org/W2097050513","https://openalex.org/W2101996922","https://openalex.org/W2103023154","https://openalex.org/W2103948957","https://openalex.org/W2127020923","https://openalex.org/W2128978199","https://openalex.org/W2130813144","https://openalex.org/W2133404041","https://openalex.org/W2164003937","https://openalex.org/W2175098281","https://openalex.org/W2475534553","https://openalex.org/W2536620281","https://openalex.org/W3023596131","https://openalex.org/W4206651839","https://openalex.org/W4234813586","https://openalex.org/W4235527302","https://openalex.org/W4244779605","https://openalex.org/W4299599836","https://openalex.org/W6660480240","https://openalex.org/W6679103854","https://openalex.org/W6679392325","https://openalex.org/W6685410096","https://openalex.org/W6721031078","https://openalex.org/W6777155463"],"related_works":["https://openalex.org/W2051058708","https://openalex.org/W1494268238","https://openalex.org/W154868527","https://openalex.org/W1983207144","https://openalex.org/W2490706771","https://openalex.org/W2480116122","https://openalex.org/W4255576661","https://openalex.org/W1516574938","https://openalex.org/W2625725254","https://openalex.org/W2563912921"],"abstract_inverted_index":{"Consider":[0],"a":[1,45,87,111,135,203,212],"dynamical":[2,93],"system":[3,132,139],"\u1e8b":[4],"=":[5,34],"f(x,":[6],"k":[7,20,37],"<sub":[8,21,38],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[9,22,39],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">0</sub>":[10,23,40],")":[11],"whose":[12],"vector":[13],"field":[14],"is":[15,106,156,183,198],"parameterized":[16],"by":[17,164,217],"real":[18,115],"parameters":[19],".":[24],"The":[25,99,180,192],"distance-to-bifurcation":[26,84,162,178,214],"problem":[27,57,85,163],"seeks":[28],"the":[29,48,64,82,119,131,144,161,166,170,177],"smallest":[30],"parameter":[31,207],"variation":[32],"\u03b3":[33],"|k":[35],"-":[36],"|":[41],"that":[42,95,157,195],"results":[43],"in":[44,176,189,211],"bifurcation":[46],"of":[47,101,114,121,130,138,143,206],"original":[49],"system's":[50,171],"phase":[51],"portrait.":[52],"Prior":[53],"work":[54],"on":[55,185],"this":[56],"used":[58],"numerical":[59],"methods":[60,69],"to":[61,109,126,168,200],"search":[62],"for":[63,91,149],"minimum":[65,83],"\u03b3,":[66],"but":[67],"these":[68],"were":[70],"computationally":[71],"demanding":[72],"and":[73,118,153],"only":[74],"guaranteed":[75],"locally":[76],"optimal":[77],"solutions.":[78],"This":[79,141],"paper":[80],"recasts":[81],"as":[86,134,173],"sum-of-squares":[88],"(SOS)":[89],"relaxation":[90],"non-negative":[92],"systems":[94,102],"have":[96],"kinetic":[97,104],"realizations.":[98],"class":[100],"with":[103],"realizations":[105,123],"large":[107],"enough":[108],"characterize":[110],"wide":[112],"range":[113],"world":[116],"applications":[117],"use":[120],"such":[122],"allows":[124],"one":[125],"find":[127],"explicit":[128],"parameterizations":[129],"Jacobian":[133,145],"rational":[136],"function":[137],"parameters.":[140],"parameterization":[142],"was":[146],"originally":[147],"proposed":[148,181],"chemical":[150],"reaction":[151],"networks":[152],"its":[154],"value":[155],"it":[158],"greatly":[159],"simplifies":[160],"removing":[165],"need":[167],"keep":[169],"equilibria":[172],"decision":[174],"variables":[175],"problem.":[179],"approach":[182,197],"illustrated":[184],"an":[186],"food":[187],"web":[188],"aquatic":[190],"eco-systems.":[191],"example":[193],"demonstrates":[194],"our":[196],"able":[199],"identify":[201],"how":[202],"coordinated":[204],"set":[205],"variations":[208],"may":[209],"result":[210],"smaller":[213],"than":[215],"predicted":[216],"competing":[218],"computational":[219],"tools.":[220]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}