Mathematical analysis of a delayed IS–LM model with general investment function

  • Driss Riad
  • Khalid Hattaf
  • Noura Yousfi
Original Research Paper


In this work, we propose a delayed IS–LM model with general investment function. The proposed model extends and generalizes many business cycle models existing in the literature. By analyzing the characteristic equation, we establish the stability of the economic equilibrium and the local existence of Hopf bifurcation. In addition, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theory.


Business cycle IS–LM model Time delay Stability Hopf Bifurcation 

Mathematics Subject Classification

34C23 34D20 37G05 91B64 



The authors would like to thank the editor and anonymous referees for their very helpful comments and suggestions that greatly improved the quality of this study.


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Copyright information

© Forum D'Analystes, Chennai 2019

Authors and Affiliations

  1. 1.Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’sikHassan II UniversityCasablancaMorocco
  2. 2.Centre Régional des Métiers de l’Education et de la Formation (CRMEF)CasablancaMorocco

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