RT Journal Article
T1 A triangle model of criminality
A1 Nuno, Juan Carlos
A1 Herrero, Miguel A.
A1 Primicerio, Mario
AB 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 histability. 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.
PB Elsevier
SN 0378-4371
YR 2008
FD 2008-05-01
LK https://hdl.handle.net/20.500.14352/50083
UL https://hdl.handle.net/20.500.14352/50083
LA eng
NO Italy–Spain Integrated Action
NO Acción Especial UCM
NO MEC
DS Docta Complutense
RD 9 abr 2025