A triangle model of criminality

Sanz Nuño, Juan Carlos; Herrero García, Miguel Ángel y 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. https://doi.org/10.1016/j.physa.2008.01.076.


Título: A triangle model of criminality
  • Sanz Nuño, Juan Carlos
  • Herrero García, Miguel Ángel
  • Primicerio, Mario
Tipo de Documento: Artículo
Título de Revista/Publicación: Physica a: Statistical Mechanics and its Applications
Fecha: Enero 2008
Volumen: 387
Palabras Clave Informales: Criminality; Nonlinear dynamics; Sociological systems.
Escuela: E.T.S.I. Montes (UPM) [antigua denominación]
Departamento: Matemática Aplicada a los Recursos Naturales [hasta 2014]
Licencias Creative Commons: Reconocimiento - Sin obra derivada - No comercial

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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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ID de Registro: 2204
Identificador DC: http://oa.upm.es/2204/
Identificador OAI: oai:oa.upm.es:2204
Identificador DOI: 10.1016/j.physa.2008.01.076
URL Oficial: http://www.sciencedirect.com/science?_ob=PublicationURL&_tockey=%23TOC%235534%232008%23996129987%23682799%23FLA%23&_cdi=5534&_pubType=J&_auth=y&_acct=C000047350&_version=1&_urlVersion=0&_userid=885385&md5=3d1db204b3c25ca0fab1cdbc0d239535
Depositado por: Memoria Investigacion
Depositado el: 18 Mar 2010 10:00
Ultima Modificación: 20 Abr 2016 11:57
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