Complexity evolution of chaotic financial systems based on fractional calculus

Abstract

Abstract Economics and finance are extremely complex nonlinear systems involving human subjects with many subjective factors. There are numerous attribute properties that cannot be described by the theory of integer-order calculus; so it is necessary to theoretically study the internal complexity of the economic and financial system using the method of bifurcation and chaos of fractional nonlinear dynamics. Fractional calculus can more accurately describe the existence characteristics of complex physical, financial or medical systems, and can truly reflect the actual state properties of these systems; therefore the application of fractional order in chaotic systems has great significance to study the mathematical analysis of nonlinear dynamic systems, and the use of fractional calculus theory to model the complexity evolution of fractional chaotic financial systems has attracted more and more scholars’ attention. On the basis of summarizing and analyzing previous studies, this paper qualitatively analyzes the stability of equilibrium solution of fractional-order chaotic financial system, and explores the complexity evolution law of the financial system near the equilibrium point and the occurring conditions of asymptotic chaotic state near this equilibrium point, and simulate the complexity evolution of chaotic financial systems using the Admas-Bashforth-Moulton finite difference method for mapping, phase diagram and time series graph. The research results of this paper provide a reference for government to formulate relevant economic policies, decision-making or further research on the complexity evolution of fractional-order chaotic financial systems.