Abstract
The interplay between criminal activity and crime control/prevention measures is inherently dynamic. This paper presents a simple nonlinear dynamical system in which criminal activity levels are coupled to policing effort. Through the process of non-dimensionalisation and sensitivity analysis, policing efficiency and the responsiveness of policing effort are identified as key parameter groupings. An analysis of the system shows that bi-stability is a feature of the dynamics. When there is no feedback between criminal activity and police recruitment, a saddle-node bifurcation occurs and threshold levels of criminal activity are required for the activity to be maintained. When feedback is permitted, we also find a backward bifurcation and criminal activity can be contained for policing efficiency below its threshold level. We demonstrate proof of concept for how the model might be used as a predictive tool with real data.
Original language | English |
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Article number | 1669 |
Journal | Mathematics |
Volume | 11 |
Issue number | 7 |
Early online date | 30 Mar 2023 |
DOIs | |
Publication status | Published - 30 Apr 2023 |
Bibliographical note
FundingThis research received no external funding.
Data Availability Statement
The Matlab and Mathematica codes used to generate figures presented in the paper are available from the corresponding author upon request.
Keywords
- bifurcations
- criminal activity
- dynamical system
- mathematical criminology
- police effort
- policing efficiency
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- Engineering (miscellaneous)
- General Mathematics