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Nonlinear Dynamics of Crime and Violence in Urban Settings

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Abstract

We perform analysis of data on crime and violence for 5,660 U.S. cities over the period of 2005-2009 and uncover the following trends: 1) The proportion of law enforcement officers required to maintain a steady low level of criminal activity increases with the size of the population of the city; 2) The number of criminal/violent events per 1,000 inhabitants of a city shows non-monotonic behavior with size of the population. We construct a dynamical model allowing for system-level, mechanistic understanding of these trends. In our model the level of rational behavior of individuals in the population is encoded into each citizen's perceived risk function. We find strong dependence on size of the population, which leads to partially irrational behavior on the part of citizens. The nature of violence changes from global outbursts of criminal/violent activity in small cities to spatio-temporally distributed, decentralized outbursts of activity in large cities, indicating that in order to maintain peace, bigger cities need larger ratio of law enforcement officers than smaller cities. We also observe existence of tipping points for communities of all sizes in the model: reducing the number of law enforcement officers below a critical level can rapidly increase the incidence of criminal/violent activity. Though surprising, these trends are in agreement with the data.

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  • Maria Fonoberova & Vladimir A. Fonoberov & Igor Mezic & Jadranka Mezic & P. Jeffrey Brantingham, 2012. "Nonlinear Dynamics of Crime and Violence in Urban Settings," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 15(1), pages 1-2.
    • Handle: RePEc:jas:jasssj:2010-80-2
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    1. Michael Makowsky, 2006. "An Agent-Based Model of Mortality Shocks, Intergenerational Effects, and Urban Crime," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 9(2), pages 1-7.
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    3. Heiko Rauhut & Marcel Junker, 2009. "Punishment Deters Crime Because Humans Are Bounded in Their Strategic Decision-Making," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(3), pages 1-1.
    4. Luís M A Bettencourt & José Lobo & Deborah Strumsky & Geoffrey B West, 2010. "Urban Scaling and Its Deviations: Revealing the Structure of Wealth, Innovation and Crime across Cities," PLOS ONE, Public Library of Science, vol. 5(11), pages 1-9, November.
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    1. Davide Secchi & Raffaello Seri, 2017. "Controlling for false negatives in agent-based models: a review of power analysis in organizational research," Computational and Mathematical Organization Theory, Springer, vol. 23(1), pages 94-121, March.
    2. Sergei Petrovskii & Weam Alharbi & Abdulqader Alhomairi & Andrew Morozov, 2020. "Modelling Population Dynamics of Social Protests in Time and Space: The Reaction-Diffusion Approach," Mathematics, MDPI, vol. 8(1), pages 1-19, January.
    3. SeHoon Lee & Jeong Hee Hong & Jang Won Bae & Il-Chul Moon, 2015. "Impact of Population Relocation to City Commerce: Micro-Level Estimation with Validated Agent-Based Model," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 18(2), pages 1-5.
    4. James Hogg & Maria Fonoberova & Igor Mezić & Ryan Mohr, 2019. "Koopman Mode Analysis of agent-based models of logistics processes," PLOS ONE, Public Library of Science, vol. 14(9), pages 1-37, September.
    5. Fonoberova, Maria & Fonoberov, Vladimir A. & Mezić, Igor, 2013. "Global sensitivity/uncertainty analysis for agent-based models," Reliability Engineering and System Safety, Elsevier, vol. 118(C), pages 8-17.
    6. Maria Fonoberova & Igor Mezić & Jadranka Mezić & Ryan Mohr, 2018. "An agent-based model of urban insurgence: Effect of gathering sites and Koopman mode analysis," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-25, October.
    7. Ignacio Ormazábal & F. A. Borotto & H. F. Astudillo, 2017. "Influence of Money Distribution on Civil Violence Model," Complexity, Hindawi, vol. 2017, pages 1-15, November.

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