Gang rivalry dynamics via coupled point process networks

M. B. Short; G. O. Mohler; P. J. Brantingham; G. E. Tita

doi:10.3934/dcdsb.2014.19.1459

Article Contents

2014, Volume 19, Issue 5: 1459-1477. Doi: 10.3934/dcdsb.2014.19.1459

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Gang rivalry dynamics via coupled point process networks

1.
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332
2.
Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, CA 95053
3.
Department of Anthropology, UCLA, Los Angeles, CA 90095
4.
Department of Criminology, Law and Society, UC Irvine, Irvine, CA 92697

Received: March 2011

Revised: June 2012

Published: July 2014

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Abstract

We introduce a point process model for inter-gang violence driven by retaliation -- a core feature of gang behavior -- and multi-party inhibition. Here, a coupled system of state-dependent jump stochastic differential equations is used to model the conditional intensities of the directed network of gang rivalries. The system admits an exact simulation strategy based upon Poisson thinning. The model produces a wide variety of transient or stationary weighted network configurations and we investigate under what conditions each type of network forms in the continuum limit. We then fit the model to gang violence data provided by the Hollenbeck district of the Los Angeles Police Department to measure the levels of excitation and inhibition present in gang violence dynamics, as well as the stability of gang rivalries in Hollenbeck.

Keywords:

Mathematics Subject Classification: 60G55, 70K50, 91D99.

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