Analysis of the Financial Chaotic Model with the Fractional Derivative Operator

Abstract

Numerical discretization for the fractional differential equations is applied to the chaotic financial model described by the Caputo derivative. The graphical representations to support the numerical discretization are presented. We profit by analyzing the impact generated by the variations of the saving rate, the per investment cost, and the elasticity of demands in the dynamics of the solutions obtained with our numerical scheme. Notably, we use bifurcation diagrams to quantify the impact of the saving rate, the per investment cost, and the elasticity of demands, as well as the Lyapunov exponent to characterize the existence of chaos for the chosen value of the fractional order. The chaos observed depends strongly on these previously mentioned parameters. We finish by proposing a suitable control to synchronize the drive system and the response fractional financial model, using Lyapunov direct methods. The stability analysis of the equilibrium points of the chaotic financial model has been presented.