2021-12-02T17:09:12Z
https://oa.upm.es/cgi/oai2
oai:oa.upm.es:2204
2016-04-20T11:57:46Z
7374617475733D707562
7375626A656374733D6D6174656D617469636173
747970653D61727469636C65
A triangle model of criminality
Sanz Nuño, Juan Carlos
Herrero García, Miguel Ángel
Primicerio, Mario
Mathematics
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.
E.T.S.I. Montes (UPM)
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
2008-01
info:eu-repo/semantics/article
Article
Physica a: Statistical Mechanics and its Applications, ISSN 0378-4371, 2008-01, Vol. 387, No. 12
PeerReviewed
application/pdf
eng
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
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physa.2008.01.076
http://oa.upm.es/2204/