Evolution of fractional-order chaotic economic systems based on non-degenerate equilibrium points

Abstract

Abstract The economic system is an irreversible entropy increase process which is constructed by many elements and is far away from the equilibrium point; and affected by various parameters change, it is quite common that its motion state appears chaotic phenomenon due to instability. The extremely complex and not completely random aperiodic motion form of chaotic phenomenon is strongly sensitive to initial conditions. The development of nonlinear science, especially the emergence and development of chaos and fractal theory, has gradually become a powerful tool for economists to study the complexity, uncertainty and nonlinearity of social economic systems; and some visionary economists began to apply the research results of nonlinear science to economics, which has produced nonlinear economics. On the basis of summarizing and analyzing previous research works, this paper first obtains the non-degenerate equilibrium point of some typical fractional-order chaotic economic systems and transforms the equilibrium points of those systems to the origin through coordinate transformation, and then analyzes the Jacobi matrixes of new systems obtained through coordinate translation, and the parameter conditions of bifurcation in the economic systems are finally given and the numerical simulation of the fractional-order chaotic economic system evolution is carried out through bifurcation diagram, phase diagram and time series diagram. The study results of this paper provide a reference for the further study of the evolution of fractional-order chaotic economic systems with non-degenerate equilibrium points.