Taming Hyperchaos with Exact Spectral Derivative Discretization Finite Difference Discretization of a Conformable Fractional Derivative Financial System with Market Confidence and Ethics Risk

Abstract

Four discrete models, using the exact spectral derivative discretization finite difference (ESDDFD) method, are proposed for a chaotic five-dimensional, conformable fractional derivative financial system incorporating ethics and market confidence. Since the system considered was recently studied using the conformable Euler finite difference (CEFD) method and found to be hyperchaotic, and the CEFD method was recently shown to be valid only at fractional index α=1, the source of the hyperchaos is in question. Through numerical experiments, illustration is presented that the hyperchaos previously detected is, in part, an artifact of the CEFD method, as it is absent from the ESDDFD models.