Export file:


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


  • Citation Only
  • Citation and Abstract

On the comparative analysis of linear and nonlinear business cycle model: Effect on system dynamics, economy and policy making in general

1 Department of Mathematics, Amity Institute of Applied Sciences, Amity University, Noida Sector-125, 201301, India
2 Department of Applied Sciences, ABV-Indian Institute of Information Technology and Management, Gwalior, Gwalior-474015, M.P., India

Research on linear and nonlinear IS-LM models has been resonating under synonymous perspectives, confined to bifurcations and intangible relations to economic work systems. Trifle discussion exists on how choice of linear/nonlinear models affects policy making and almost no elaboration on framing an economic system within a linear and nonlinear structure to analyze their effect separately. Parameters surrounding IS-LM model like adjustment coefficients, depreciation of capital stock etc. have not been given due spotlight, given the audacity they possess to modulate system dynamics. In counteraction, we have investigated an augmented IS-LM model with two-time delays in capital accumulation equation. This model is subjected to linear and nonlinear arguments of investment, savings and liquidity function giving rise to M1(linear) and M2(nonlinear) models. They undergo hopf bifurcation for different values of delay parameters τ1 and τ2. Our study accentuates the following aspects(1) In a neophyte attempt, comparing the dynamics of a linear and nonlinear business cycle model in an environment as similar as possible, when τ1 and τ2 are the bifurcating parameters. (2) Parameter sensitivity analysis for both models. (3) Non linearity in savings function, which is a sparse event so far. Our findings reveal that (1) Non-linearity elevates system sensitivity and M2 model attains stability easily in the long run for dual delays, while for single delay M1 model has this feat. (2) M2 model encapsulates recurring cyclic behavior while M1 model is not capable of generating the same and demonstrates motifs of either stability or instability. (3) Parameter sensitivity analysis reveals that both the models are most vulnerable when (3a)Value of depreciation of capital stock is decreased. (3b) Money supply and propensities to investment are increased. (4) how aforementioned information can be utilized for crafting economic policies for linear/nonlinear economies, especially curated for their modus operandi. Numerical simulations follow.
  Article Metrics


1. Abta A, Kaddar A, Alaoui HT (2008) Stability of Limit Cycle in a Delayed IS-LM Business Cycle model. Appl Math Sci 2: 2459-2471.

2. Ahmed M (2005) How well does the IS-LM model fit in a developing economy: The case of India. Int J Appl Econ 2: 90-106.

3. Apergis N, Eleftheriou S (2016) Gold returns: Do business cycle asymmetries matter? Evidence from an international country sample. Econ Model 57: 164-170.

4. Ballestra LV, Guerrini L, Pacelli G (2013) Stability Switches and Hopf Bifurcation in a Kaleckian Model of Business Cycle. Abstract and Applied Analysis, Hindawi, 1-8.

5. Cai J (2005) Hopf bifurcation in the IS-LM business cycle model with time delay. Electron J Differ Equations, 1-6.

6. Cooke KL, Grossman Z (1982) Discrete delay, distributed delay and stability switches. J Math Anal Appl 86: 592-627.    

7. De Cesare L, Sportelli M (2005) A dynamic IS-LM model with delayed taxation revenues. Chaos Solitons Fractals 25: 233-244.    

8. Hale JK (1971) Functional differential equations, New York: Springer-Verlag.

9. Hassard BD, Kazarinoff ND, Wan YH (1981) Theory and Application of Hopf Bifurcation, Cambridge University Press, Cambridge.

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

11. Kaddar A, Alaoui HT (2008) Fluctuations in a mixed IS-LM business cycle model. Electron J Differ Equations 2: 1-9.

12. Kaddar A, Alaoui HT (2008) On the dynamic behavior of a delayed IS-LM business cycle model. Appl Math Sci 2: 1529-1539.

13. Keynes' Liquidity Preference Theory of Interest Rate Determination (2016). Economics Discussion. Available from: http://www.economicsdiscussion.net/keynesian-economics/keynes-theory/keynes-liquidity-preference-theory-of-interest-rate-\determination/17187.

14. Li S (2019) Hopf bifurcation, stability switches and chaos in a prey-predator system with three stage structure and two time delays. Math Biosci Eng 16: 6934-6961.    

15. Lopes AS, Zsurkis GF (2019) Are linear models really unuseful to describe business cycle data? Appl Econ 51: 2355-2376.    

16. Peng M, Zhang Z (2018) Hopf bifurcation analysis in a predator-prey model with two time delays and stage structure for the prey. Adv Differ Equations 2018.

17. Riad D, Hattaf K, Yousfi N (2019) Mathematical analysis of a delayed IS-LM model with general investment function. J Anal 27: 1047-1064.    

18. Rocsoreanu C, Sterpu M (2009) Bifurcation in a nonlinear business cycle model. Romai J 5: 145-152.

19. Ruan S, Wei J (2003) On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dyn Contin Discrete Impulsive Syst Series A 10: 863-874.

20. Song Y, Wei J (2004) Bifurcation analysis for Chen's system with delayed feedback and its application to control of chaos. Chaos Solitons Fractals 22: 75-91.    

21. Turnovsky SJ (2019) Trends and fads in macroeconomic dynamics. Indian Econ Rev 54: 179-197.    

22. Wang ZH (2012) A Very Simple Criterion For Characterizing The Crossing Direction Of Time-Delay Systems With Delay-Dependent Parameters. Int J Bifurcation Chaos 22: 1250048.    

23. Zak PJ (1999) Kaleckian Lags in General Equilibrium. Rev Polit Econ 11: 321-330.    

24. Zhang Z, Bi Q (2012) Bifurcation In A Piecewise Linear Circuit With Switching Boundaries. Int J Bifurcation Chaos 22: 1250034.    

25. Zhou L, Li Y (2009) A dynamic IS-LM business cycle model with two time delays in capital accumulation equation. J Comput Appl Math 228: 182-187.    

© 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