Stability of an unemployment model with a non-linear job creation
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Keywords:
Unemployment model, Global asymptotic stability, Geometric approach, Nonlinear dynamicsAbstract
This study introduces a mathematical model for unemployment that incorporates nonlinear functions in the matching process and job creation. Derived from observed data and constraints on job creation, the nonlinearity enhances the model’s realism. Through a geometric approach, sufficient conditions are identified to ensure a successful application of global stability analysis. The dynamics of the general system, including thresholds and global stability of the nontrivial equilibrium, are fully determined. Existence and stability of both trivial and non-trivial equilibria are rigorously proven using Lyapunov functions, Jacobian matrices, and the Lozinski measure. Numerical analysis illustrates the theoretical findings, emphasizing the global asymptotic stability of the nontrivial equilibrium under specific conditions. This work offers valuable insights into unemployment dynamics, bridging complex mathematics with practical economic models.
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