Quasi-Periodicity & Period-Halving bifurcation Routes to Chaos in a Financial Model

Abstract

This paper aims to study the complex nonlinear dynamics involved in the financial system, depending on three key parameters: saving amount, the cost associated with unit investment and elasticity of commodity demand. This research explores the formation of a chaotic attractor by altering a parameter within the financial model. We illustrated that a Hopf bifurcation takes place, resulting in the emergence of a stable limit cycle. Previous studies have not addressed the quasi periodicity and period halving bifurcation. Through numerical analysis, we have uncovered a cascade of period halving bifurcation, quasi periodicity which led to the formation of a strange attractor. The existence of chaos in the system has been effectively recognized using various methods, including bifurcation diagrams, lyapunov Dimension, lyapunov Exponents, time series and, two dimensional and three-dimensional phase portraits. The system's sensitivity is estimated utilizing the fourth order Runge-Kutta method.