AIMS Mathematics, 2020, 5(4): 3321-3330. doi: 10.3934/math.2020213

Research article

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Dynamical analysis of Kaldor business cycle model with variable depreciation rate of capital stock

School of Mathematics and Statistics, Qilu University of Technology(Shandong Academy of Sciences), Jinan 250353, China

In this paper, the Kaldor business cycle model with variable depreciation rate of the capital stock are investigate the existence, uniqueness and stability of the positive equilibrium point, and the existence of the periodic solution and Hopf bifurcation respectively. Finally, we analyze the dynamic behaviors of the specific system and perform numerical simulations.
  Figure/Table
  Supplementary
  Article Metrics

References

1. N. Kaldor, A model of the trade cycle, Econ. J., 50 (1940), 78-92.    

2. W. W. Chang, D. J. Smyth, The existence and persistence of cycles in a non-linear model: Kaldor's 1940 model re-examined, Rev. Econ. Study., 38 (1971), 37-44.    

3. J. Grasman, J. J. Wentzel, Co-existence of a limit cycle and an equilibrium in kaldor's business cycle model and its consequences, J. Econ. Behav. Organ., 24 (1994), 369-377.    

4. K. Hattaf, D. Riad, N. Yousfi, A generalized business cycle model with delays in gross product and capital stock, Chaos Soliton. Fract., 98 (2017), 31-37.    

5. A. Krawiec, M. Szydlowski, The Kaldor-Kalecki business cycle model, Ann. Oper. Res., 89 (1999), 89-100.    

6. X. P. Wu, Codimension-2 bifurcations of the Kaldor model of business cycle, Chaos Soliton. Fract., 44 (2011), 28-42.    

7. S. Chatterjee, Capital utilization, economic growth and convergence, J. Econ. Dyn. Control., 29 (2005), 2093-2124.    

8. E. Angelopoulou, S. Kalyvitis, Estimating the Euler equation for aggregate investment with endogenous capital depreciation, South. Econ. J., 78 (2012), 1057-1078.    

9. M. Ishaq Nadiri, I. R. Prucha, Estimation of the depreciation rate of physical and R&D capital in the U.S. total manufacturing sector, Econ. Inq., 34 (1996), 43-56.    

10. Z. Ma, Y. Zhou, Qualitative and Stable Methods for Ordinary Differential Equations, Science Press, Beijing, 2001.

11. J. Zhang, B. Feng, Geometric Theory and Bifurcation Problem of Ordinary Differential Equations, 2 Eds., Peking University Press, Beijing, 2000.

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved