@article{Martínez-Farías_Alvarado-Sánchez_Rangel-Cortes_Hernández-Hernández_2022, title={Bi-dimensional crime model based on anomalous diffusion with law enforcement effect}, volume={2}, url={https://mmnsa.org/index.php/mmnsa/article/view/19}, DOI={10.53391/mmnsa.2022.01.003}, abstractNote={<p>Several models based on discrete and continuous fields have been proposed to comprehend residential criminal dynamics. This study introduces a two-dimensional model to describe residential burglaries diffusion, employing Lèvy flights dynamics. A continuous model is presented, introducing bidimensional fractional operator diffusion and its differences with the 1-dimensional case. Our results show, graphically, the hotspot’s existence solution in a 2-dimensional attractiveness field, even fractional derivative order is modified. We also provide qualitative evidence that steady-state approximation in one dimension by series expansion is insufficient to capture similar original system behavior. At least for the case where series coefficients have a linear relationship with derivative order. Our results show, graphically, the hotspot’s existence solution in a 2-dimensional attractiveness field, even if fractional derivative order is modified. Two dynamic regimes emerge in maximum and total attractiveness magnitude as a result of fractional derivative changes, these regimes can be understood as considerations about different urban environments. Finally, we add a Law enforcement component, embodying the "Cops on dots" strategy; in the Laplacian diffusion dynamic, global attractiveness levels are significantly reduced by Cops on dots policy but lose efficacy in Lèvy flight-based diffusion regimen. The four-step Preditor-Corrector method is used for numerical integration, and the fractional operator is approximated, getting the advantage of the spectral methods to approximate spatial derivatives in two dimensions.</p>}, number={1}, journal={Mathematical Modelling and Numerical Simulation with Applications}, author={Martínez-Farías, Francisco Javier and Alvarado-Sánchez, Anahí and Rangel-Cortes, Eduardo and Hernández-Hernández, Arturo}, year={2022}, month={Jan.}, pages={26–40} }