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Global Stability Analysis of a Five-Dimensional Unemployment Model with Distributed Delay

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  • Eva Kaslik

    (Department of Mathematics and Computer Science, West University of Timişoara, 300223 Timișoara, Romania
    Institute for Advanced Environmental Research, West University of Timişoara, Bd. V. Pârvan nr. 4, 300223 Timişoara, Romania
    These authors contributed equally to this work.)

  • Mihaela Neamţu

    (Department of Economics and Business Administration, West University of Timişoara, 300223 Timişoara, Romania
    These authors contributed equally to this work.)

  • Loredana Flavia Vesa

    (Department of Mathematics and Computer Science, West University of Timişoara, 300223 Timișoara, Romania
    Institute for Advanced Environmental Research, West University of Timişoara, Bd. V. Pârvan nr. 4, 300223 Timişoara, Romania
    These authors contributed equally to this work.)

Abstract

The present paper proposes a five-dimensional mathematical model for studying the labor market, focusing on unemployment, migration, fixed term contractors, full time employment and the number of available vacancies. The distributed time delay is considered in the rate of change of available vacancies that depends on the past regular employment levels. The non-dimensional mathematical model is introduced and the existence of the equilibrium points is analyzed. The positivity and boundedness of solutions are provided and global asymptotic stability findings are presented both for the employment free equilibrium and the positive equilibrium. The numerical simulations support the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3037-:d:688988
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. 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).

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