On fractional discrete financial system: Bifurcation, chaos, and control

Abstract

The dynamic analysis of systems financial is a developed field that combines mathematics and economics to understand and explain fluctuations in financial markets. This paper introduces a new three-dimensional fractional financial map, we dissection of its nonlinear dynamics system under commensurate and incommensurate orders. Such, we evaluate when the equilibrium points are stable or unstable at various fractional order further we use many numerical methods, phase plots in 2D and 3D projections, bifurcation diagram and maximum Lyapunov exponent. These techniques reveal that the financial map exhibits chaotic attractor. This study grounded on the Caputo-like discrete operator, specifically influenced by the variance of the commensurate and incommensurate orders. Furthermore, we confirm the presence and measure complexity of chaos in the financial map by 0-1 test and the approximate entropy algorithm. Additionally, we offer non-linear type controllers so that to stabilize the fractional financial map. Finally, the numerical results of this study was done using MATLAB.