{"id":"https://openalex.org/W2146596734","doi":"https://doi.org/10.1142/s0218127409024700","title":"BIFURCATIONS AND CHAOS IN A PERIODICALLY PROBED COMPUTER NETWORK","display_name":"BIFURCATIONS AND CHAOS IN A PERIODICALLY PROBED COMPUTER NETWORK","publication_year":2009,"publication_date":"2009-09-01","ids":{"openalex":"https://openalex.org/W2146596734","doi":"https://doi.org/10.1142/s0218127409024700","mag":"2146596734"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127409024700","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409024700","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/A5053541740","display_name":"Ian Frommer","orcid":null},"institutions":[{"id":"https://openalex.org/I186274478","display_name":"United States Coast Guard Academy","ror":"https://ror.org/01y922f71","country_code":"US","type":"education","lineage":["https://openalex.org/I186274478"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"IAN FROMMER","raw_affiliation_strings":["US Coast Guard Academy, New London, CT 06320, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"US Coast Guard Academy, New London, CT 06320, USA","institution_ids":["https://openalex.org/I186274478"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004842043","display_name":"Eric Harder","orcid":null},"institutions":[{"id":"https://openalex.org/I1330347796","display_name":"United States Department of Defense","ror":"https://ror.org/0447fe631","country_code":"US","type":"government","lineage":["https://openalex.org/I1330347796"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"ERIC HARDER","raw_affiliation_strings":["US Department of Defense, College Park, MD 20742, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"US Department of Defense, College Park, MD 20742, USA","institution_ids":["https://openalex.org/I1330347796"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019387364","display_name":"Brian R. Hunt","orcid":"https://orcid.org/0000-0003-0779-9866"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"BRIAN HUNT","raw_affiliation_strings":["University of Maryland, College Park, MD 20742, USA","University of Maryland, College Park, MD 20742 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Maryland, College Park, MD 20742, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"University of Maryland, College Park, MD 20742 USA","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069727852","display_name":"Ryan Lance","orcid":null},"institutions":[{"id":"https://openalex.org/I1330347796","display_name":"United States Department of Defense","ror":"https://ror.org/0447fe631","country_code":"US","type":"government","lineage":["https://openalex.org/I1330347796"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"RYAN LANCE","raw_affiliation_strings":["US Department of Defense, College Park, MD 20742, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"US Department of Defense, College Park, MD 20742, USA","institution_ids":["https://openalex.org/I1330347796"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082913931","display_name":"Edward Ott","orcid":"https://orcid.org/0000-0002-9395-5062"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"EDWARD OTT","raw_affiliation_strings":["University of Maryland, College Park, MD 20742, USA","University of Maryland, College Park, MD 20742 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Maryland, College Park, MD 20742, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"University of Maryland, College Park, MD 20742 USA","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022360238","display_name":"James A. Yorke","orcid":"https://orcid.org/0000-0002-9599-0136"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"JAMES YORKE","raw_affiliation_strings":["University of Maryland, College Park, MD 20742, USA","University of Maryland, College Park, MD 20742 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Maryland, College Park, MD 20742, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"University of Maryland, College Park, MD 20742 USA","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4734,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.67203459,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"19","issue":"09","first_page":"3129","last_page":"3141"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9973999857902527,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9973999857902527,"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/T10138","display_name":"Network Traffic and Congestion Control","score":0.9861999750137329,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9836000204086304,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.664242148399353},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5938434600830078},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5910627245903015},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5858417749404907},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5558915734291077},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5125126838684082},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5027620792388916},{"id":"https://openalex.org/keywords/predictability","display_name":"Predictability","score":0.4710540473461151},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4558079242706299},{"id":"https://openalex.org/keywords/network-packet","display_name":"Network packet","score":0.44818899035453796},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4142833948135376},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3946200907230377},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.36694657802581787},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.32918447256088257},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.31895026564598083},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2220456302165985},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.146305650472641},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1213829517364502},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.1116405725479126},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09612128138542175}],"concepts":[{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.664242148399353},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5938434600830078},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5910627245903015},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5858417749404907},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5558915734291077},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5125126838684082},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5027620792388916},{"id":"https://openalex.org/C197640229","wikidata":"https://www.wikidata.org/wiki/Q2534066","display_name":"Predictability","level":2,"score":0.4710540473461151},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4558079242706299},{"id":"https://openalex.org/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.44818899035453796},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4142833948135376},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3946200907230377},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36694657802581787},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.32918447256088257},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.31895026564598083},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2220456302165985},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.146305650472641},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1213829517364502},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.1116405725479126},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09612128138542175},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127409024700","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409024700","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1536934246","https://openalex.org/W1569474751","https://openalex.org/W1585188069","https://openalex.org/W1619647493","https://openalex.org/W1869912679","https://openalex.org/W1990920914","https://openalex.org/W1994717387","https://openalex.org/W2010181515","https://openalex.org/W2021929396","https://openalex.org/W2038782040","https://openalex.org/W2040317361","https://openalex.org/W2061614940","https://openalex.org/W2078318318","https://openalex.org/W2079241154","https://openalex.org/W2089230062","https://openalex.org/W2102495174","https://openalex.org/W2110416206","https://openalex.org/W2121667323","https://openalex.org/W2124478678","https://openalex.org/W2124559247","https://openalex.org/W2124920704","https://openalex.org/W2130583399","https://openalex.org/W2134414695","https://openalex.org/W2138804494","https://openalex.org/W2147837310","https://openalex.org/W2155291040","https://openalex.org/W2158359711","https://openalex.org/W2158733823","https://openalex.org/W2232175550","https://openalex.org/W2994517056","https://openalex.org/W3001942212","https://openalex.org/W4248483556","https://openalex.org/W4251229883","https://openalex.org/W4255193292"],"related_works":["https://openalex.org/W2803635921","https://openalex.org/W2378563815","https://openalex.org/W2077160835","https://openalex.org/W2387815769","https://openalex.org/W2024426258","https://openalex.org/W2460205926","https://openalex.org/W2292858622","https://openalex.org/W2025856057","https://openalex.org/W1979383579","https://openalex.org/W937853716"],"abstract_inverted_index":{"In":[0],"this":[1,137],"paper":[2],"we":[3,45,122],"model":[4,85],"a":[5,37,53,67,87,113,120],"computer":[6],"network":[7],"consisting":[8],"of":[9,23,35,55,69,71,79,99,115],"one":[10,15],"standard":[11],"Internet":[12],"connection":[13,17,30],"and":[14,103,129],"nonstandard":[16,29],"that":[18,74],"transmits":[19],"uniformly":[20],"sized":[21],"bursts":[22],"packets":[24],"at":[25],"regular":[26],"intervals.":[27],"The":[28],"can":[31],"represent":[32],"probing":[33,57],"activity":[34],"either":[36],"diagnostic":[38],"measurement":[39],"or":[40],"attack.":[41],"Using":[42],"bifurcation":[43,101],"diagrams,":[44],"study":[46],"how":[47],"the":[48,56,76,80,97,100,116,131],"network's":[49,81],"behavior":[50],"changes":[51],"as":[52],"function":[54],"frequency.":[58],"These":[59],"diagrams":[60],"reveal":[61],"interesting,":[62],"nonintuitive":[63],"behavior.":[64,82],"We":[65],"present":[66],"series":[68],"models":[70],"increasing":[72],"simplicity":[73],"capture":[75],"significant":[77],"features":[78],"Our":[83],"simplest":[84],"is":[86],"piecewise":[88],"linear,":[89],"discontinuous":[90],"one-dimensional":[91],"map.":[92],"This":[93],"map":[94],"helps":[95],"explain":[96],"structure":[98],"diagram,":[102],"allows":[104],"us":[105],"to":[106,125],"directly":[107],"determine":[108],"Lyapunov":[109],"exponents,":[110],"which":[111],"give":[112],"measure":[114],"system's":[117],"predictability.":[118],"As":[119],"result,":[121],"are":[123],"able":[124],"more":[126],"precisely":[127],"describe":[128],"categorize":[130],"dynamics,":[132],"including":[133],"chaos,":[134],"exhibited":[135],"by":[136],"network.":[138]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}