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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Adaptation of an ecological territorial model to street gang spatial patterns in Los Angeles

Pages: 3223 - 3244, Volume 32, Issue 9, September 2012      doi:10.3934/dcds.2012.32.3223

 
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Laura M. Smith - University of California Los Angeles, Department of Mathematics, 520 Portola Plaza Box 951555, Los Angeles, CA 90095-1555, United States (email)
Andrea L. Bertozzi - University of California Los Angeles, Department of Mathematics, 520 Portola Plaza Box 951555, Los Angeles, CA 90095-1555, United States (email)
P. Jeffrey Brantingham - University of California Los Angeles, Department of Anthropology, 375 Portola Plaza, 341 Haines Hall, Box 951553, Los Angeles, CA 90095-1553, United States (email)
George E. Tita - University of California Irvine, Department of Criminology, Law and Society, 2340 Social Ecology II, Irvine, CA 92697-7080, United States (email)
Matthew Valasik - University of California Irvine, Department of Criminology, Law and Society, 2340 Social Ecology II, Irvine, CA 92697-7080, United States (email)

Abstract: Territorial behavior is often found in nature. Coyotes and wolves organize themselves around a den site and mark their territory to distinguish their claimed region. Moorcroft et al. model the formation of territories and spatial distributions of coyote packs and their markings in [31]. We modify this ecological approach to simulate spatial gang dynamics in the Hollenbeck policing division of eastern Los Angeles. We incorporate important geographical features from the region that would inhibit movement, such as rivers and freeways. From the gang and marking densities created by this method, we create a rivalry network from overlapping territories and compare the graph to both the observed network and those constructed through other methods. Data on the locations of where gang members have been observed is then used to analyze the densities created by the model.

Keywords:  Partial differential equations, ecological territory, spatial patterns, networks, densities.
Mathematics Subject Classification:  Primary: 35Q80, 91D25; Secondary: 91D10, 91D30, 92F05.

Received: December 2011;      Revised: March 2012;      Available Online: April 2012.

 References