Turing Instability and Spatial Pattern Formation in a Model of Urban Crime

Isabella Torcicollo and Maria Vitiello ()
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Isabella Torcicollo: Istituto per le Applicazioni del Calcolo “M. Picone”, CNR, Via Pietro Castellino 111, 80131 Naples, Italy
Maria Vitiello: Dipartimento di Meccanica, Matematica e Management (DMMM), Politecnico di Bari, Via Orabona 4, 70126 Bari, Italy

Mathematics, 2024, vol. 12, issue 7, 1-15

Abstract: A nonlinear crime model is generalized by introducing self- and cross-diffusion terms. The effect of diffusion on the stability of non-negative constant steady states is applied. In particular, the cross-diffusion-driven instability, called Turing instability, is analyzed by linear stability analysis, and several Turing patterns driven by the cross-diffusion are studied through numerical investigations. When the Turing–Hopf conditions are satisfied, the type of instability highlighted in the ODE model persists in the PDE system, still showing an oscillatory behavior.

Keywords: crime model; self- and cross-diffusion; stability analysis; Turing patterns; Turing–Hopf bifurcation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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