IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v98y2017icp121-129.html
   My bibliography  Save this article

Dynamical analysis of a model of social behavior: Criminal vs non-criminal population

Author

Listed:
  • Abbas, Syed
  • Tripathi, Jai Prakash
  • Neha, A.A.

Abstract

In this paper, we construct a model motivated by the well known predator-prey model to study the interaction between criminal population and non-criminal population. Our aim is to study various possibilities of interactions between them. First we model it using simple predator-prey model, then we modify it by considering the logistic growth of non-criminal population. We clearly deduce that the model with logistic growth is better than classical one. More precisely, the role of carrying capacity on the dynamics of criminal minded population is discussed. Further, we incorporate law enforcement term in the model and study its effect. The result obtained suggest that by incorporating enforcement law, the criminal population reduces from the very beginning, which resembles with real life situation. Our result indicates that the criminal minded population exist as long as coefficient of enforcement lc does not cross a threshold value and after this value the criminal minded population extinct. In addition, we also discuss the occurrence of saddle-node bifurcation in case of model system with law enforcement. Numerical examples and simulations are presented to illustrate the obtained results.

Suggested Citation

  • Abbas, Syed & Tripathi, Jai Prakash & Neha, A.A., 2017. "Dynamical analysis of a model of social behavior: Criminal vs non-criminal population," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 121-129.
    • Handle: RePEc:eee:chsofr:v:98:y:2017:i:c:p:121-129
    DOI: 10.1016/j.chaos.2017.03.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917300802
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.03.027?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gary S. Becker, 1974. "Crime and Punishment: An Economic Approach," NBER Chapters, in: Essays in the Economics of Crime and Punishment, pages 1-54, National Bureau of Economic Research, Inc.
    2. M. B. Gordon & J. R. Iglesias & V. Semeshenko & J. P. Nadal, 2009. "Crime and punishment: the economic burden of impunity," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 68(1), pages 133-144, March.
    3. 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.
    4. Iglesias, J.R. & Semeshenko, V. & Schneider, E.M. & Gordon, M.B., 2012. "Crime and punishment: Does it pay to punish?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3942-3950.
    5. Steven D. Levitt, 1996. "The Effect of Prison Population Size on Crime Rates: Evidence from Prison Overcrowding Litigation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 111(2), pages 319-351.
    6. Fajnzylber, Pablo & Lederman, Daniel & Loayza, Norman, 2002. "What causes violent crime?," European Economic Review, Elsevier, vol. 46(7), pages 1323-1357, July.
    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. Sooknanan, Joanna & Seemungal, Terence A.R., 2023. "Criminals and their models - a review of epidemiological models describing criminal behaviour," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    2. Luo, Demou, 2021. "Global bifurcation for a reaction–diffusion predator–prey model with Holling-II functional response and prey–taxis," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

    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. 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).
    2. Alves, Luiz G.A. & Ribeiro, Haroldo V. & Rodrigues, Francisco A., 2018. "Crime prediction through urban metrics and statistical learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 435-443.
    3. Entorf, H. & Winker, P., 2008. "Investigating the drugs-crime channel in economics of crime models: Empirical evidence from panel data of the German States," International Review of Law and Economics, Elsevier, vol. 28(1), pages 8-22, March.
    4. 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.
    5. 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.
    6. Lauridsen, Jørgen T. & Zeren, Fatma & Ari, Ay?E, 2015. "Is Crime in Turkey Economically Rational?/¿Es económicamente racional el crimen en Turquía?," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 33, pages 37-52, Enero.
    7. 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.
    8. Hunt, Jennifer, 2006. "Do Teen Births Keep American Crime High?," Journal of Law and Economics, University of Chicago Press, vol. 49(2), pages 533-566, October.
    9. 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.
    10. 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.
    11. Eugene Braslavskiy & Firmin Doko Tchatoka & Virginie Masson, 2019. "The Importance Of Punishment Substitutability In Criminometric Studies," Bulletin of Economic Research, Wiley Blackwell, vol. 71(3), pages 491-507, July.
    12. 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.
    13. Mohamad Kassem & Amjad Ali & Marc Audi, 2019. "Unemployment Rate, Population Density and Crime Rate in Punjab (Pakistan): An Empirical Analysis," Bulletin of Business and Economics (BBE), Research Foundation for Humanity (RFH), vol. 8(2), pages 92-104, June.
    14. Javier Núñez & Jorge Rivera & Xavier Villavicencio & Oscar Molina, 2003. "Determinantes socioeconómicos y demográficos del crimen en Chile," Estudios de Economia, University of Chile, Department of Economics, vol. 30(1 Year 20), pages 55-85, June.
    15. Angela K. Dills & Jeffrey A. Miron & Garrett Summers, 2010. "What Do Economists Know about Crime?," NBER Chapters, in: The Economics of Crime: Lessons For and From Latin America, pages 269-302, National Bureau of Economic Research, Inc.
    16. Horst Entorf & Peter Winker, 2001. "The Economics of Crime: Investigating the Drugs-Crime Channel," Law and Economics 0108001, University Library of Munich, Germany.
    17. Leo H. Kahane & David Paton & Rob Simmons, 2008. "The Abortion–Crime Link: Evidence from England and Wales," Economica, London School of Economics and Political Science, vol. 75(297), pages 1-21, February.
    18. Lauridsen, Jørgen T. & Zeren, Fatma & Ari, Ayse, 2014. "Is crime in Turkey economically rational?," Discussion Papers on Economics 3/2014, University of Southern Denmark, Department of Economics.
    19. Saridakis George, 2013. "Shop Crime and Deterrence: Evidence on Shoplifting among Young People in the Youth Lifestyle Survey (YLS)," Review of Law & Economics, De Gruyter, vol. 9(2), pages 197-237, September.
    20. Guido Travaglini, 2003. "Property Crime and Law Enforcement in Italy. A Regional Panel Analysis 1980-95," Giornale degli Economisti, GDE (Giornale degli Economisti e Annali di Economia), Bocconi University, vol. 62(2), pages 211-240, October.

    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:eee:chsofr:v:98:y:2017:i:c:p:121-129. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.