A triangle model of criminality

Sanz Nuño, Juan Carlos and Herrero García, Miguel Ángel and Primicerio, Mario (2008). A triangle model of criminality. "Physica a: Statistical Mechanics and its Applications", v. 387 (n. 12); pp. 2926-2936. ISSN 0378-4371.


Title: A triangle model of criminality
  • Sanz Nuño, Juan Carlos
  • Herrero García, Miguel Ángel
  • Primicerio, Mario
Item Type: Article
Título de Revista/Publicación: Physica a: Statistical Mechanics and its Applications
Date: January 2008
Volume: 387
Freetext Keywords: Criminality; Nonlinear dynamics; Sociological systems.
Faculty: E.T.S.I. Montes (UPM)
Department: Matemática Aplicada a los Recursos Naturales [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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This paper is concerned with a quantitative model describing the interaction of three sociological species, termed as owners, criminals and security guards, and denoted by X, Y and Z respectively. In our model, Y is a predator of the species X, and so is Z with respect to Y . Moreover, Z can also be thought of as a predator of X, since this last population is required to bear the costs of maintaining Z. We propose a system of three ordinary differential equations to account for the time evolution of X(t), Y (t) and Z(t) according to our previous assumptions. Out of the various parameters that appear in that system, we select two of them, denoted by H, and h, which are related with the efficiency of the security forces as a control parameter in our discussion. To begin with, we consider the case of large and constant owners population, which allows us to reduce (3)–(5) to a bidimensional system for Y (t) and Z(t). As a preliminary step, this situation is first discussed under the additional assumption that Y (t) + Z(t) is constant. A bifurcation study is then performed in terms of H and h, which shows the key role played by the rate of casualties in Y and Z, that results particularly in a possible onset of bistability. When the previous restriction is dropped, we observe the appearance of oscillatory behaviours in the full two-dimensional system. We finally provide a exploratory study of the complete model (3)–(5), where a number of bifurcations appear as parameter H changes, and the corresponding solutions behaviours are described.

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Item ID: 2204
DC Identifier: http://oa.upm.es/2204/
OAI Identifier: oai:oa.upm.es:2204
Deposited by: Memoria Investigacion
Deposited on: 18 Mar 2010 10:00
Last Modified: 20 Apr 2016 11:57
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