Time Delay Stabilizes Chaos Dynamics in Economic System

Rashmi Bhardwaj; Anamika Ranjan

doi:https://doi.org/10.14445/22315373/IJMTT-V53P563

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 53 | Number 7 | Year 2018 | Article Id. IJMTT-V53P563 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P563

Time Delay Stabilizes Chaos Dynamics in Economic System

Rashmi Bhardwaj, Anamika Ranjan

Citation :

Rashmi Bhardwaj, Anamika Ranjan, "Time Delay Stabilizes Chaos Dynamics in Economic System," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 7, pp. 515-524, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P563

Abstract

This paper discusses the role of time delay feedback which stabilizes the chaos of nonlinear financial model. The interest rate, investment demand and price index are modelled with the help of saving amount, cost per investment, demand elasticity of commercial markets and the strength of feedback. All these parameters are considered to be positive. The stability of financial model is studied by Routh-Hurwitz criterion. The distributed time delay feedback strength stabilized the unstable financial system. Bifurcation of parameter and Lypunove exponent is simulated for time delay feedback system. Using the numerical method, it is observed that the inappropriate combination of saving amount, cost per investment and elasticity of investment demand of commercial market in the financial system is the root cause of chaos. The unstable system is stabilized by introducing the distributed time delay feedback strength. The stability and chaotic behaviour of systems gives the condition and behaviour of economic implications. It is concluded that the system is chaotic and to ensure stability of state, it is controlled by time delay feedback controlled system.

Keywords

Nonlinear financial system, Distributed time delay, chaos, Routh-Hurwitz criterion, Lypunove exponent, Bifurcation and equilibrium point.

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