Global asymptotic stability of an unemployment model using geometric approach
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Keywords:
Unemployment model; Nonlinear employment rate; Global stability; Geometric approachAbstract
In this work, we study the global asymptotic stability of a nonlinear unemployment model. The nonlinearity comes from the matching process between vacancies and unemployed people. Thus, we assume that the employment rate is a general nonlinear function, which includes the bilinear form presented in the previous scientific research. We provide conditions that guarantee the existence and
uniqueness of a positive equilibrium. To study the dynamic behavior of this equilibrium, we propose Li’s geometrical approach. This technique ensures global asymptotic stability without the need to impose an additional condition. Finally, we provide numerical illustrations of our study.
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