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

Author

Listed:
  • Isabella Torcicollo

    (Istituto per le Applicazioni del Calcolo “M. Picone”, CNR, Via Pietro Castellino 111, 80131 Naples, Italy
    These authors contributed equally to this work.)

  • Maria Vitiello

    (Dipartimento di Meccanica, Matematica e Management (DMMM), Politecnico di Bari, Via Orabona 4, 70126 Bari, Italy
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Isabella Torcicollo & Maria Vitiello, 2024. "Turing Instability and Spatial Pattern Formation in a Model of Urban Crime," Mathematics, MDPI, vol. 12(7), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1097-:d:1370779
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    References listed on IDEAS

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    3. Nuño, Juan C. & Herrero, Miguel A. & Primicerio, Mario, 2008. "A triangle model of criminality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2926-2936.
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