{"id":"https://openalex.org/W2050274271","doi":"https://doi.org/10.1137/090759069","title":"Nonlinear Patterns in Urban Crime: Hotspots, Bifurcations, and Suppression","display_name":"Nonlinear Patterns in Urban Crime: Hotspots, Bifurcations, and Suppression","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2050274271","doi":"https://doi.org/10.1137/090759069","mag":"2050274271"},"language":"en","primary_location":{"id":"doi:10.1137/090759069","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090759069","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","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/A5015300785","display_name":"Martin B. Short","orcid":"https://orcid.org/0000-0002-3890-3163"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"M. B. Short","raw_affiliation_strings":["Department of Mathematics, UCLA, Los Angeles, CA 90095"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, CA 90095","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090707978","display_name":"Andrea L. Bertozzi","orcid":"https://orcid.org/0000-0003-0396-7391"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. L. Bertozzi","raw_affiliation_strings":["Department of Mathematics, UCLA, Los Angeles, CA 90095"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, CA 90095","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080042065","display_name":"P. Jeffrey Brantingham","orcid":"https://orcid.org/0000-0003-1079-0053"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. J. Brantingham","raw_affiliation_strings":["Department of Anthropology, UCLA, Los Angeles, CA 90095"],"affiliations":[{"raw_affiliation_string":"Department of Anthropology, UCLA, Los Angeles, CA 90095","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015300785"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":null,"apc_paid":null,"fwci":6.6938,"has_fulltext":false,"cited_by_count":144,"citation_normalized_percentile":{"value":0.96697596,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"9","issue":"2","first_page":"462","last_page":"483"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9768999814987183,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hotspot","display_name":"Hotspot (geology)","score":0.7756456136703491},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7518147230148315},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.5489195585250854},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5384623408317566},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.5178945064544678},{"id":"https://openalex.org/keywords/supercritical-fluid","display_name":"Supercritical fluid","score":0.48975086212158203},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.39549803733825684},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3790782392024994},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36868157982826233},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36388063430786133},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3111502528190613},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.16205576062202454},{"id":"https://openalex.org/keywords/geophysics","display_name":"Geophysics","score":0.1160748302936554}],"concepts":[{"id":"https://openalex.org/C146481406","wikidata":"https://www.wikidata.org/wiki/Q105131","display_name":"Hotspot (geology)","level":2,"score":0.7756456136703491},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7518147230148315},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.5489195585250854},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5384623408317566},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.5178945064544678},{"id":"https://openalex.org/C118419359","wikidata":"https://www.wikidata.org/wiki/Q682585","display_name":"Supercritical fluid","level":2,"score":0.48975086212158203},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.39549803733825684},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3790782392024994},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36868157982826233},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36388063430786133},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3111502528190613},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.16205576062202454},{"id":"https://openalex.org/C8058405","wikidata":"https://www.wikidata.org/wiki/Q46255","display_name":"Geophysics","level":1,"score":0.1160748302936554},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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":3,"locations":[{"id":"doi:10.1137/090759069","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090759069","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.157.863","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.157.863","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucla.edu/~bertozzi/papers/weaklynonlinear_sub.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.210.4362","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.210.4362","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucla.edu/~bertozzi/papers/SIADS2010.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.7799999713897705}],"awards":[{"id":"https://openalex.org/G2300623714","display_name":"DHB: Mathematical and Simulation Modeling of Crime Hot Spots","funder_award_id":"0527388","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7320824963","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306078","funder_display_name":"U.S. Department of Defense"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306078","display_name":"U.S. Department of Defense","ror":"https://ror.org/0447fe631"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W577139908","https://openalex.org/W1495014989","https://openalex.org/W1537028224","https://openalex.org/W1569482464","https://openalex.org/W1602351032","https://openalex.org/W1663318879","https://openalex.org/W1833129238","https://openalex.org/W1935768838","https://openalex.org/W1970674026","https://openalex.org/W1974767491","https://openalex.org/W1977578104","https://openalex.org/W1980661496","https://openalex.org/W1980812171","https://openalex.org/W1990159953","https://openalex.org/W2002849130","https://openalex.org/W2007850214","https://openalex.org/W2019900294","https://openalex.org/W2029107725","https://openalex.org/W2040443526","https://openalex.org/W2042892258","https://openalex.org/W2056583384","https://openalex.org/W2066764855","https://openalex.org/W2078234004","https://openalex.org/W2086126894","https://openalex.org/W2086473239","https://openalex.org/W2093010986","https://openalex.org/W2095244803","https://openalex.org/W2101665746","https://openalex.org/W2106104958","https://openalex.org/W2113908404","https://openalex.org/W2134904490","https://openalex.org/W2136416382","https://openalex.org/W2149577899","https://openalex.org/W2151113508","https://openalex.org/W2155458379","https://openalex.org/W2161594278","https://openalex.org/W2167073771","https://openalex.org/W2167618408","https://openalex.org/W2275865526","https://openalex.org/W2962848199","https://openalex.org/W3101860975","https://openalex.org/W4241557574"],"related_works":["https://openalex.org/W2246258018","https://openalex.org/W4296238711","https://openalex.org/W3105759999","https://openalex.org/W2513783521","https://openalex.org/W2713021514","https://openalex.org/W2544244289","https://openalex.org/W2159473547","https://openalex.org/W2762201087","https://openalex.org/W2356929285","https://openalex.org/W2018908229"],"abstract_inverted_index":{"Abstract.":[0],"We":[1,79],"present":[2,80],"a":[3,19],"weakly":[4],"nonlinear":[5],"analysis":[6],"of":[7,15,30,64,93,109,121],"our":[8,36,56,86],"recently":[9],"developed":[10],"model":[11],"for":[12],"the":[13,28,40,48,62,91,103,118],"formation":[14],"crime":[16,31],"patterns.":[17],"Using":[18],"perturbative":[20],"approach,":[21],"we":[22,59,101],"find":[23],"amplitude":[24],"equations":[25],"that":[26,67,83],"govern":[27],"development":[29],"\u201chotspot":[32],"\u201d":[33],"patterns":[34],"in":[35,38,55,127],"system":[37],"both":[39,84],"1D":[41],"and":[42,89],"2D":[43],"cases.":[44],"In":[45],"addition":[46],"to":[47,53,113],"supercritical":[49],"spots":[50],"already":[51],"shown":[52],"exist":[54],"previous":[57],"work,":[58],"prove":[60],"here":[61],"existence":[63,92],"subcritical":[65,70,95],"hotspots":[66,96,110],"arise":[68],"via":[69],"pitchfork":[71],"bifurcations":[72],"or":[73],"transcritical":[74],"bifurcations,":[75],"depending":[76],"on":[77],"geometry.":[78],"numerical":[81],"results":[82],"validate":[85],"analytical":[87],"findings":[88],"confirm":[90],"these":[94,106],"as":[97],"stable":[98],"states.":[99],"Finally,":[100],"examine":[102],"differences":[104],"between":[105],"two":[107],"types":[108],"with":[111],"regard":[112],"attempted":[114],"hotspot":[115],"suppression,":[116],"referencing":[117],"varying":[119],"levels":[120],"success":[122],"such":[123],"attempts":[124],"have":[125],"had":[126],"real":[128],"world":[129],"scenarios.":[130]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":10}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
