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  4. Dynamics of a diffusive business cycle model with two delays and variable depreciation rate

Dynamics of a diffusive business cycle model with two delays and variable depreciation rate

MMC.
2024;
Volume 11, Number 3
: pp. 617–630
https://doi.org/10.23939/mmc2024.03.617
Received: October 15, 2023
Revised: July 08, 2024
Accepted: July 12, 2024

Lasfar S., Hattaf K., Yousfi N.  Dynamics of a diffusive business cycle model with two delays and variable depreciation rate.  Mathematical Modeling and Computing. Vol. 11, No. 3, pp. 617–630 (2024)

Authors:
  1. S. Lasfar
  2. K. Hattaf
  3. N. Yousfi
1
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca
2
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca; Equipe de Recherche en Modélisation et Enseignement des Mathématiques (ERMEM), Centre Régional des Métiers de l'Education et de la Formation (CRMEF)
3
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca

The main aim of this work is to analyze the dynamics of a delayed business cycle model described by partial differential equations (PDEs) in order to take into account the depreciation rate of capital stock and the diffusion effect.  Firstly, the existence of solutions and the economic equilibrium are carefully studied.  Secondly, the local stability and the existence of Hopf bifurcation are established.  Finally, some numerical simulations are presented to illustrate the analytical results.

business cycle
depreciation rate
diffusion effect
Hopf bifurcation
stability
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