Search

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. [ABSTRACT FROM AUTHOR]

This paper considers a mixed duopoly competition model, in which two enterprises produce heterogeneous commodities and compete for output in the same market. One enterprise separates the ownership from the management rights, and the enterprise owner entrusts a manager to manage the enterprise. The other enterprise considers consumer surplus. Through stability theory and numerical simulation, the local stability of each equilibrium point and the way the system performs bifurcation are analyzed. By using the basin of attraction, the global stability of the system is studied. The multistability is explained and the properties and some phenomena of the basin of attraction and the chaotic attractor are analyzed by using the knowledge of noninvertible map and critical curve. Finally, the influence of parameters on enterprise profit and objective is also analyzed, which is helpful for enterprises to make decisions in the process of game. • A mixed duopoly Cournot competition model is established based on heterogeneous products. • The complex dynamic behavior of the economic system is analyzed by means of chaos theory and numerical simulation. • The complex structures of the basin of attraction and chaotic attractor are studied by using noninvertible map. • The influence of the parameters on the average objective and the average profit of the two enterprises is analyzed. [ABSTRACT FROM AUTHOR]