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. https://doi.org/10.1016/j.physa.2008.01.076.

Description

Title: A triangle model of criminality
Author/s:
  • 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
ISSN: 0378-4371
Volume: 387
Subjects:
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

Full text

[img]
Preview
PDF - Requires a PDF viewer, such as GSview, Xpdf or Adobe Acrobat Reader
Download (361kB) | Preview

Abstract

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.

  • Logo InvestigaM (UPM)
  • Logo GEOUP4
  • Logo Open Access
  • Open Access
  • Logo Sherpa/Romeo
    Check whether the anglo-saxon journal in which you have published an article allows you to also publish it under open access.
  • Logo Dulcinea
    Check whether the spanish journal in which you have published an article allows you to also publish it under open access.
  • Logo de Recolecta
  • Logo del Observatorio I+D+i UPM
  • Logo de OpenCourseWare UPM