Stability analysis of an unemployment model with time delay

Tawatchai Petaratip; Piyapong Niamsup; Tawatchai Petaratip; Piyapong Niamsup

doi:10.3934/math.2021434

AIMS Mathematics

2021, Volume 6, Issue 7: 7421-7440. doi: 10.3934/math.2021434

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Research article

Stability analysis of an unemployment model with time delay

Tawatchai Petaratip ¹,
Piyapong Niamsup ^{1,2
,
,}

1.
Department of Mathematics, Chiang Mai University, Chiang Mai 50200, Thailand
2.
Research Center in Mathematics and Applied Mathematics Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received: 04 November 2020 Accepted: 22 April 2021 Published: 06 May 2021
MSC : 34D20, 34D23, 34K20

In this paper, we have developed and analyzed an unemployment model of differential equations with time delay, taking into consideration the role of government for the support of vacancies creation. We investigated the dynamic behavior of the model system and carried out a stability analysis. Conditions for the nonexistence of delay induced instability and the local asymptotic stability of the positive equilibrium points are derived. Moreover, sufficient conditions for global asymptotic stability of the positive equilibrium points are obtained. Numerical results have been given to show the effectiveness of the theoretical results.
- mathematical model,
- unemployment,
- time delay,
- global stability,
- Lyapunov functional
Citation: Tawatchai Petaratip, Piyapong Niamsup. Stability analysis of an unemployment model with time delay[J]. AIMS Mathematics, 2021, 6(7): 7421-7440. doi: 10.3934/math.2021434

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Abstract

In this paper, we have developed and analyzed an unemployment model of differential equations with time delay, taking into consideration the role of government for the support of vacancies creation. We investigated the dynamic behavior of the model system and carried out a stability analysis. Conditions for the nonexistence of delay induced instability and the local asymptotic stability of the positive equilibrium points are derived. Moreover, sufficient conditions for global asymptotic stability of the positive equilibrium points are obtained. Numerical results have been given to show the effectiveness of the theoretical results.

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