IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i7p1097-d1370779.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/7/1097/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/7/1097/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Entorf, Horst & Spengler, Hannes, 2000. "Socioeconomic and demographic factors of crime in Germany: Evidence from panel data of the German states," International Review of Law and Economics, Elsevier, vol. 20(1), pages 75-106, March.
    2. Pritam, Kocherlakota Satya & Sugandha, & Mathur, Trilok & Agarwal, Shivi, 2021. "Underlying dynamics of crime transmission with memory," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Abayomi Ayotunde Ayoade & Oluwatayo Michael Ogunmiloro & Srinivasarao Thota, 2024. "Mathematical modeling and analysis of the influence of family background on the spread of crime," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(6), pages 5899-5920, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bansal, Komal & Mathur, Trilok & Agarwal, Shivi, 2023. "Fractional-order crime propagation model with non-linear transmission rate," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Tripathi, Jai Prakash & Bugalia, Sarita & Burdak, Kavita & Abbas, Syed, 2021. "Dynamical analysis and effects of law enforcement in a social interaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    3. Raphael, Steven & Winter-Ember, Rudolf, 2001. "Identifying the Effect of Unemployment on Crime," Journal of Law and Economics, University of Chicago Press, vol. 44(1), pages 259-283, April.
    4. Entorf, Horst & Spengler, Hannes, 2000. "Socioeconomic and demographic factors of crime in Germany: Evidence from panel data of the German states," International Review of Law and Economics, Elsevier, vol. 20(1), pages 75-106, March.
    5. Blesse, Sebastian & Diegmann, André, 2022. "The place-based effects of police stations on crime: Evidence from station closures," Journal of Public Economics, Elsevier, vol. 207(C).
    6. Armin Falk & Andreas Kuhn & Josef Zweimüller, 2011. "Unemployment and Right‐wing Extremist Crime," Scandinavian Journal of Economics, Wiley Blackwell, vol. 113, pages 260-285, June.
    7. Edmark, Karin, 2003. "The Effects of Unemployment on Property Crime: Evidence from a Period of Unusually Large Swings in the Business Cycle," Working Paper Series 2003:14, Uppsala University, Department of Economics.
    8. Demougin, Dominique & Schwager, Robert, 2003. "Law enforcement and criminality: Europe vs. USA," International Review of Law and Economics, Elsevier, vol. 23(2), pages 217-225, June.
    9. Lauridsen, Jørgen & Nannerup, Niels & Skak, Morten, 2013. "Does Owner-Occupied Housing Affect Neighbourhood Crime?," Discussion Papers on Economics 19/2013, University of Southern Denmark, Department of Economics.
    10. Entorf, Horst, 2005. "Islamistischer Terrorismus : Analysen, Entwicklungen und Anti-Terrorpolitik aus der Sicht ökonomischer Forschung," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 24551, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    11. George Saridakis, 2004. "Violent Crime in the United States of America: A Time-Series Analysis Between 1960–2000," European Journal of Law and Economics, Springer, vol. 18(2), pages 203-221, September.
    12. Randi Hjalmarsson & Stephen Machin & Paolo Pinotti, 2024. "Crime and the labor market," CEP Discussion Papers dp2044, Centre for Economic Performance, LSE.
    13. Raul Caruso & Adelaide Baronchelli, 2013. "Economic aspects of the complementarity between corruption and crime: evidence from Italy in the period 1996-2005," International Journal of Monetary Economics and Finance, Inderscience Enterprises Ltd, vol. 6(2/3), pages 244-260.
    14. Sebastian Leitner, 2015. "Effects of Income Inequality on Population Health and Social Outcomes at the Regional Level in the EU," wiiw Working Papers 113, The Vienna Institute for International Economic Studies, wiiw.
    15. Horst Entorf & Hannes Spengler, 2005. "Ökonometrie der Kriminalität," ifo Schnelldienst, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, vol. 58(16), pages 13-25, August.
    16. Entorf, Horst & Winkler, Peter, 2001. "The economics of crime: investigating the drugs-crime channel: empirical evidence from panel data of the German states," ZEW Discussion Papers 01-37, ZEW - Leibniz Centre for European Economic Research.
    17. Roee Sarel, 2022. "Crime and punishment in times of pandemics," European Journal of Law and Economics, Springer, vol. 54(2), pages 155-186, October.
    18. Mindaugas Butkus & Kristina Matuzevièi?t? & Alma Maèiulyt?-Šniukien?, 2019. "Do Economic Conditions Still Cause Crime? Some Comforting Empirical Evidences from EU Panel," Zbornik radova Ekonomskog fakulteta u Rijeci/Proceedings of Rijeka Faculty of Economics, University of Rijeka, Faculty of Economics and Business, vol. 37(2), pages 603-628.
    19. Entorf, Horst & Meyer, Susanne, 2004. "Kosten und Nutzen des Strafvollzuges : Grundlagen im Rahmen einer rationalen Kriminalpoltik," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 20450, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    20. Denis Fougère & Francis Kramarz & Julien Pouget, 2009. "Youth Unemployment and Crime in France," Journal of the European Economic Association, MIT Press, vol. 7(5), pages 909-938, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1097-:d:1370779. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.