Application and research of fractional differential equations in dynamic analysis of supply chain financial chaotic system

This paper first introduces the numerical solution of fractional differential equations and the method of discriminating chaos, which lays a mathematical foundation for the later study of fractional-order chaotic systems. Secondly, the thesis uses the theoretical knowledge of fractional differential to construct a new three-dimensional supply chain fractional differential game model. The numerical simulation analysis of the complex dynamic behavior of the model is carried out to investigate the influence of the output adjustment velocity parameters on the dynamic behavior of the system. The parameter control method is used to chaotic control of the multi-period bifurcation and unstable periodic orbit of the producer's production decision, so that the chaotic model is re-stabilized to the Nash equilibrium state. Finally, the paper constructs a new financial model of fractional time delay and analyzes the basic dynamics of the system in detail. In addition, the stability analysis of the system is carried out by using Lyapunov stability theory, and then the controller is designed to realize the chaotic control of the system, which provides theoretical guidance for the stable development of the financial market. (C) 2019 Elsevier Ltd. All rights reserved.