Modeling the dynamics of business cycle with general investment and variable depreciation rate of capital stock

Volume 29, Issue 3, pp 264--271 https://doi.org/10.22436/jmcs.029.03.05

Publication Date: November 01, 2022 Submission Date: May 08, 2022 Revision Date: August 05, 2022 Accteptance Date: August 18, 2022

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Authors

S. Lasfar - Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences, Ben M'Sick Hassan II University of Casablanca, P.O Box 7955 Sidi Othman, Casablanca, Morocco. E. M. Warrak - Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences, Ben M'Sick Hassan II University of Casablanca, P.O Box 7955 Sidi Othman, Casablanca, Morocco. Kh. Hattaf - Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences, Ben M'Sick Hassan II University of Casablanca, P.O Box 7955 Sidi Othman, Casablanca, Morocco. - Equipe de Recherche en Modelisation et Enseignement des Mathematiques (ERMEM), Centre Regional des Metiers de l'Education et de la Formation (CRMEF) , 20340 Derb Ghalef, Casablanca, Morocco. N. Yousfi - Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences, Ben M'Sick Hassan II University of Casablanca, P.O Box 7955 Sidi Othman, Casablanca, Morocco.

Abstract

In this paper, we develop a business cycle model with general investment, variable depreciation rate of capital stock and two delays. The first delay describes the time lag between the decision of investment and its implementation, while the second one models the time lag for investment to be produced. The well-posedness and the existence of economic equilibrium are carefully investigated. Moreover, the stability of the economic equilibrium and the existence of Hopf bifurcation are established. The case when the two delays are equal is rigourously studied.

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Keywords

• Business cycle
• depreciation
• time delays
• stability
• Hopf bifurcation

MSC

•  34D20
•  34C23
•  91B55

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