IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v212y2023icp122-137.html
   My bibliography  Save this article

Assessing the impact of escalating attacks on soft targets by criminal gang: A modelling viewpoint using bifurcation analysis

Author

Listed:
  • Aliyu, Major Murtala Bello
  • Baidu, Ali Audu
  • Abdulhamid, Bala Ma’aji
  • Ibrahim, Mohammed Olanrewaju
  • Mukhtar, Fu’ad Muhammad

Abstract

The emerging threat of criminal gangs in society has severe consequences on the socio-economic well-being of individuals. To examine the impact of morally upright individuals and attacks on soft targets (i.e., vulnerable members of the society) on the coexistence dynamics of the society, we employ a system of ordinary differential equations (ODE) where individuals in the community are allowed to mix and interact. In the co-dimension one bifurcation analysis, we discover the emergence of supercritical and subcritical Hopf bifurcation, transcritical bifurcation, and saddle–node bifurcation of cycle. To understand how these different attractors interact and mediate a crime-free society, we conduct a co-dimension two bifurcation analysis (i.e., by using the morally upright individuals (h1) and attacks on soft target (e) as our bifurcation parameter). The interplay between morally upright individuals and attacks on soft targets shows the presence of a global attractor (i.e., Generalized Hopf bifurcation), which serves as a synchronization centre for the model. Several studies have reported the emergence of stable limit cycles in the criminal gang model. However, we discover a transition from stable to unstable limit cycles when the attacks on soft targets are considered under distinct coexistence factors. This study revealed that morally upright individuals and attacks on soft targets positively affected the coexistence dynamics of society. Furthermore, we observed that an unstable limit cycle is a causative factor for chaotic dynamics in the non-linear system. We further noted that the positive effect of morally upright individuals plays a crucial role in mediating a stable and crime-free society. The study concluded that the recruitment rate of susceptible individuals to the criminal gang has little consequence on the peaceful coexistence of society if the society maintains high morality.

Suggested Citation

  • Aliyu, Major Murtala Bello & Baidu, Ali Audu & Abdulhamid, Bala Ma’aji & Ibrahim, Mohammed Olanrewaju & Mukhtar, Fu’ad Muhammad, 2023. "Assessing the impact of escalating attacks on soft targets by criminal gang: A modelling viewpoint using bifurcation analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 122-137.
    • Handle: RePEc:eee:matcom:v:212:y:2023:i:c:p:122-137
    DOI: 10.1016/j.matcom.2023.04.030
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423002008
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.04.030?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. Sooknanan, J. & Comissiong, D.M.G., 2018. "A mathematical model for the treatment of delinquent behaviour," Socio-Economic Planning Sciences, Elsevier, vol. 63(C), pages 60-69.
    2. Ohene Opoku, Nicholas Kwasi-Do & Bader, Georg & Fiatsonu, Edem, 2021. "Controlling crime with its associated cost during festive periods using mathematical techniques," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    3. Sun, Chengjun & Lin, Yiping & Tang, Shoupeng, 2007. "Global stability for an special SEIR epidemic model with nonlinear incidence rates," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 290-297.
    4. 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)

    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. 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. Gao, Qingwu & Zhuang, Jun, 2020. "Stability analysis and control strategies for worm attack in mobile networks via a VEIQS propagation model," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    3. 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.
    4. Yuri M. Zhukov, 2014. "Theory of Indiscriminate Violence," Working Paper 365551, Harvard University OpenScholar.
    5. Bansal, Komal & Mathur, Trilok & Agarwal, Shivi, 2023. "Fractional-order crime propagation model with non-linear transmission rate," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    6. Ganguly, Prasangsha & Mukherjee, Sayanti, 2021. "A multifaceted risk assessment approach using statistical learning to evaluate socio-environmental factors associated with regional felony and misdemeanor rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    7. 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).
    8. Naim, Mouhcine & Lahmidi, Fouad & Namir, Abdelwahed & Kouidere, Abdelfatah, 2021. "Dynamics of an fractional SEIR epidemic model with infectivity in latent period and general nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    9. Santoprete, Manuele, 2019. "Countering violent extremism: A mathematical model," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 314-329.
    10. Alves, Luiz G.A. & Ribeiro, Haroldo V. & Mendes, Renio S., 2013. "Scaling laws in the dynamics of crime growth rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(11), pages 2672-2679.
    11. Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "Transmission dynamics of tuberculosis with multiple re-infections," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    12. Khan, Asaf & Zaman, Gul, 2018. "Global analysis of an age-structured SEIR endemic model," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 154-165.
    13. Qi, Ke & Liu, Zhijun & Wang, Lianwen & Chen, Yuming, 2023. "Global dynamics of a diffusive SEICR HCV model with nonlinear incidences," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 181-197.
    14. Alsenafi, Abdulaziz & Barbaro, Alethea B.T., 2018. "A convection–diffusion model for gang territoriality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 765-786.
    15. Cai, Liming & Wu, Jingang, 2009. "Analysis of an HIV/AIDS treatment model with a nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 175-182.

    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:matcom:v:212:y:2023:i:c:p:122-137. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.