Fractal Analysis And Chaotic Control Of A Type Of Economic Competing System

With the rapid development of global economy and modern science and technology,the traditional theory of economics based on linear system theory is faced with great challenge because of the evolution of complex economic systems.The traditional econo-my advocates certainty and balance,believing that the economic system will remain in a quiescent state without the intervention of external conditions,which makes the tradi-tional economics has been unable to explain the economic phenomena in some complex dynamic characteristics.But fractal theory and chaos make relatively reasonable expla-nation to these phenomena.Fractal and chaos start from "unbalance" and analyze the complex,fuzzy and uncertain economic system,which opens up a new way for the study of economics.In this paper,the fractal analysis and chaotic control of the output duopoly competing evolution model are discussed.Based on the early oligopoly model,this model provides the model foundation for the research of many experts and scholars in the later period.Firstly,Julia set of the economic model is introduced by use of the ideas and methods of Julia set in fractal geometry,and the condition for the stability of the fixed point is given.The feedback control is also taken on the Julia set of the model.Synchronization of two different Julia sets of the model with different parameters is discussed.Secondly,a step backward control method and optimal function control model are introduced into the control,and the box dimension of Julia sets under different control method are also calculated,which describing the complexity of the Julia set.Finally,based on the definition and its stability of the passive system,the passive control items are designed to the output of the duopoly competition evolution model.And then the optimal control function are used for the anti-chaos control,combining with the two results,this paper introduced the idea of game theory.The chaotic game of the system is introduced by combining the chaos control and anti-control.