scholarly journals Hopf Bifurcation in an Augmented IS-LM Linear Business Cycle Model with Two Time Delays

2020 ◽  
Vol 5 (3) ◽  
pp. 518-528
Author(s):  
Firdos Karim ◽  
Sudipa Chauhan ◽  
Sumit Kaur Bhatia ◽  
Joydip Dhar
Keyword(s):  
Hopf Bifurcation ◽  
Business Cycle ◽  
Capital Accumulation ◽  
Local Stability ◽  
Time Delays ◽  
Equilibrium Points ◽  
Scale Production ◽  
Cycle Model ◽  
Investment Function ◽  
Business Cycle Model

This paper deals with the amalgamated basic IS-LM business cycle model with Kaldor’s growth model to form an augmented model. Pertaining to substantial evidence, IS-LM model in paradigm with a specific economic extension (Kaldor-Kalecki Business cycle model in our case) provides an adept explanation of a developing but strong economy like that of our country. Occurring in the equation of capital accumulation, the two time delays are a result of the assumption in the investment function being both income and capital stock dependent in past period and maturity period. Investigating a model combined with capital accumulation is both interesting and important. From economist point of view, production without capital is impossible to even imagine. Moreover capital accumulation is impeccable to large-scale production, specialisation and creation of employment opportunities. In our model ‘I’ the investment function, ‘S’ the savings function and ‘L’ the demand for money are depending linearly on their arguments. We adhere to a linear model, contrary to the popular belief of non- linear models being the undisputed style for modern economics. The model is first shown to be mathematically and economically poised. The local stability of boundary and interior equilibrium points has been investigated. Three cases arise, pertaining to two time delays. System dynamics exhibits mutation under the influence of time delays and may clinch or discharge its local stability when subjected to the latter. Hopf bifurcation occurs when the delay parameter crosses a critical value.

scholarly journals Global Existence of Periodic Solutions in a Delayed Kaldor-Kalecki Model

2009 ◽  
Vol 14 (4) ◽  
pp. 463-472 ◽  
Author(s):  
A. Kaddar ◽  
H. Talibi Alaoui
Keyword(s):  
Hopf Bifurcation ◽  
Global Existence ◽  
Business Cycle ◽  
Periodic Solutions ◽  
Cycle Model ◽  
Global Hopf Bifurcation ◽  
Numerical Examples ◽  
Existence Of Periodic Solutions ◽  
Business Cycle Model ◽  
Theoretical Results

This paper is concerned with a delayed Kaldor-Kalecki non-linear business cycle model in income. By applying a global Hopf bifurcation result due to Wu, the global existence of periodic solutions is investigated. Numerical examples will be given in the end, to illustrate our theoretical results.

scholarly journals Local Hopf Birurcation and Stability of Limit Cycle in a Delayed Kaldor-Kalecki Model

2009 ◽  
Vol 14 (3) ◽  
pp. 333-343 ◽  
Author(s):  
A. Kaddar ◽  
H. Talibi Alaoui
Keyword(s):  
Hopf Bifurcation ◽  
Business Cycle ◽  
Periodic Solutions ◽  
Limit Cycle ◽  
Cycle Model ◽  
Explicit Algorithm ◽  
Local Hopf Bifurcation ◽  
Business Cycle Model ◽  
The Stability

We consider a delayed Kaldor-Kalecki business cycle model. We first consider the existence of local Hopf bifurcation, and we establish an explicit algorithm for determining the direction of the Hopf bifurcation and the stability or instability of the bifurcating branch of periodic solutions using the methods presented by O. Diekmann et al. in [1]. In the end, we conclude with an application.

scholarly journals Hopf Bifurcation Analysis in a Delayed Kaldor-Kalecki Model of Business Cycle

2008 ◽  
Vol 13 (4) ◽  
pp. 439-449 ◽  
Author(s):  
A. Kaddar ◽  
H. Talibi Alaoui
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Business Cycle ◽  
Bifurcation Analysis ◽  
Capital Stock ◽  
Capital Accumulation ◽  
Local Stability ◽  
Critical Value

In this paper, we analyze the model of business cycle with time delay set forth by A. Krawiec and M. Szydłowski [1]. Our goal in this model is to introduce the time delay into capital stock and gross product in capital accumulation equation. The dynamics are studied in terms of local stability and of the description of the Hopf bifurcation, that is proven to exist as the delay (taken as a parameter of bifurcation) cross some critical value. Additionally we conclude with an application.

scholarly journals Stability and Hopf Bifurcation Analysis on a Nonlinear Business Cycle Model

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Liming Zhao ◽  
Zhipei Zhao
Keyword(s):  
Hopf Bifurcation ◽  
Business Cycle ◽  
Stable Region ◽  
Market Regulation ◽  
Three Dimension ◽  
Cycle Model ◽  
Macroeconomic Policies ◽  
Theoretical Understanding ◽  
Reported Study ◽  
Business Cycle Model

This study begins with the establishment of a three-dimension business cycle model based on the condition of a fixed exchange rate. Using the established model, the reported study proceeds to describe and discuss the existence of the equilibrium and stability of the economic system near the equilibrium point as a function of the speed of market regulation and the degree of capital liquidity and a stable region is defined. In addition, the condition of Hopf bifurcation is discussed and the stability of a periodic solution, which is generated by the Hopf bifurcation and the direction of the Hopf bifurcation, is provided. Finally, a numerical simulation is provided to confirm the theoretical results. This study plays an important role in theoretical understanding of business cycle models and it is crucial for decision makers in formulating macroeconomic policies as detailed in the conclusions of this report.

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