IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v185y2021icp535-546.html
   My bibliography  Save this article

Global stability analysis of an unemployment model with distributed delay

Author

Listed:
  • Kaslik, Eva
  • Neamţu, Mihaela
  • Vesa, Loredana Flavia

Abstract

A mathematical model with distributed time delay describing the labour market is investigated, focusing on the asymptotic stability of the unique positive equilibrium point. The positivity and boundedness of the solutions are proved and the local stability analysis reveals that the positive equilibrium point is asymptotically stable, regardless of the distributed time delay considered in the model. Moreover, the construction of a suitable Lyapunov function leads to global asymptotic stability results. Numerical simulations are presented with the aim of substantiating the theoretical statements.

Suggested Citation

  • Kaslik, Eva & Neamţu, Mihaela & Vesa, Loredana Flavia, 2021. "Global stability analysis of an unemployment model with distributed delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 535-546.
    • Handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:535-546
    DOI: 10.1016/j.matcom.2021.01.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421000112
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.01.010?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. Yu, Jinchen & Peng, Mingshu, 2016. "Stability and bifurcation analysis for the Kaldor–Kalecki model with a discrete delay and a distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 66-75.
    2. Hallegatte, Stéphane & Ghil, Michael & Dumas, Patrice & Hourcade, Jean-Charles, 2008. "Business cycles, bifurcations and chaos in a neo-classical model with investment dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 57-77, July.
    3. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2018. "Stationary distribution and extinction of a stochastic predator–prey model with additional food and nonlinear perturbation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 226-239.
    4. Liliana Harding & Mihaela Neamţu, 2018. "A Dynamic Model of Unemployment with Migration and Delayed Policy Intervention," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 427-462, March.
    5. Adimy, Mostafa & Crauste, Fabien & Halanay, Andrei & Neamţu, Mihaela & Opriş, Dumitru, 2006. "Stability of limit cycles in a pluripotent stem cell dynamics model," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1091-1107.
    6. Matsumoto, Akio & Szidarovszky, Ferenc, 2011. "Delay differential neoclassical growth model," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 272-289, May.
    7. Fanelli, Viviana & Maddalena, Lucia, 2020. "A nonlinear dynamic model for credit risk contagion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 45-58.
    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. Culda, Loredana Camelia & Kaslik, Eva & Neamţu, Mihaela, 2022. "Stability and bifurcations in a general Cournot duopoly model with distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Eva Kaslik & Mihaela Neamţu & Anca Rădulescu, 2022. "Preface to the Special Issue on “Advances in Differential Dynamical Systems with Applications to Economics and Biology”," Mathematics, MDPI, vol. 10(19), pages 1-3, September.
    3. Eva Kaslik & Mihaela Neamţu & Loredana Flavia Vesa, 2021. "Global Stability Analysis of a Five-Dimensional Unemployment Model with Distributed Delay," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
    4. Njike-Tchaptchet, Eric Rostand & Tadmon, Calvin, 2023. "Mathematical modeling of the unemployment problem in a context of financial crisis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 241-262.

    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. Eva Kaslik & Mihaela Neamţu & Loredana Flavia Vesa, 2021. "Global Stability Analysis of a Five-Dimensional Unemployment Model with Distributed Delay," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
    2. Culda, Loredana Camelia & Kaslik, Eva & Neamţu, Mihaela, 2022. "Stability and bifurcations in a general Cournot duopoly model with distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Kaslik, Eva & Neamţu, Mihaela, 2020. "Dynamics of a tourism sustainability model with distributed delay," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    4. Peng, Miao & Zhang, Zhengdi & Qu, Zifang & Bi, Qinsheng, 2020. "Qualitative analysis in a delayed Van der Pol oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    5. Oluwatayo Michael Ogunmiloro & Adesoji Abraham Obayomi & Gazali Oluwasegun Agboola, 2024. "The Menace of Ghost Workers, Job Racketeers, and Creators of Online Job Offer Scam Sites on Unemployment in Nigeria: A Mathematical Model Analysis and Control," SN Operations Research Forum, Springer, vol. 5(2), pages 1-38, June.
    6. Hallegatte, Stéphane & Dumas, Patrice, 2009. "Can natural disasters have positive consequences? Investigating the role of embodied technical change," Ecological Economics, Elsevier, vol. 68(3), pages 777-786, January.
    7. Gomes, Orlando, 2013. "Information stickiness on general equilibrium and endogenous cycles," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 7, pages 1-43.
    8. Gori, Luca & Guerrini, Luca & Sodini, Mauro, 2015. "A continuous time Cournot duopoly with delays," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 166-177.
    9. Hallegatte, Stéphane & Ghil, Michael, 2008. "Natural disasters impacting a macroeconomic model with endogenous dynamics," Ecological Economics, Elsevier, vol. 68(1-2), pages 582-592, December.
    10. Bottani, Samuel & Grammaticos, Basile, 2008. "A simple model of genetic oscillations through regulated degradation," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1468-1482.
    11. Andreas Groth & Michael Ghil & Stéphane Hallegatte & Patrice Dumas, 2015. "The role of oscillatory modes in US business cycles," OECD Journal: Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2015(1), pages 63-81.
    12. Shaikhet, Leonid, 2023. "Stability of equilibria of exponential type system of three differential equations under stochastic perturbations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 105-117.
    13. Cao, Nan & Fu, Xianlong, 2023. "Stationary distribution and extinction of a Lotka–Volterra model with distribute delay and nonlinear stochastic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    14. Elena Olmedo, 2014. "Forecasting Spanish Unemployment Using Near Neighbour and Neural Net Techniques," Computational Economics, Springer;Society for Computational Economics, vol. 43(2), pages 183-197, February.
    15. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Stationary distribution of a regime-switching predator–prey model with anti-predator behaviour and higher-order perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 199-210.
    16. Singh, Vimal, 2007. "Modified LMI condition for the realization of limit cycle-free digital filters using saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1448-1453.
    17. Matsumoto, Akio & Szidarovszky, Ferenc, 2012. "Nonlinear delay monopoly with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 507-519.
    18. Kemp-Benedict, Eric, 2012. "The national bioenergy investment model: Technical documentation," MPRA Paper 37835, University Library of Munich, Germany.
    19. Kim, Sangkwon & Park, Jintae & Lee, Chaeyoung & Jeong, Darae & Choi, Yongho & Kwak, Soobin & Kim, Junseok, 2020. "Periodic travelling wave solutions for a reaction-diffusion system on landscape fitted domains," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    20. Pimentel, Carlos Eduardo Hirth & Rodriguez, Pablo M. & Valencia, Leon A., 2020. "A note on a stage-specific predator–prey stochastic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).

    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:185:y:2021:i:c:p:535-546. 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.