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

Abstract

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.

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Acknowledgements

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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Correspondence to Khalid Hattaf.

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Riad, D., Hattaf, K. & Yousfi, N. Mathematical analysis of a delayed IS–LM model with general investment function. J Anal 27, 1047–1064 (2019). https://doi.org/10.1007/s41478-018-0161-y

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Keywords

  • Business cycle
  • IS–LM model
  • Time delay
  • Stability
  • Hopf Bifurcation

Mathematics Subject Classification

  • 34C23
  • 34D20
  • 37G05
  • 91B64