Fractal Dynamics Analysis Of Discrete Competition Model And Its Application

In recent years,the dynamic research of competition model has been widely used in the fields of economy,finance,ecology,supply chain management and so on.The dynamic research of competition model refers to the dynamic simulation and analysis of the mathematical model which can describe the relationship of competition game,and qualitative and quantitative analysis of the coupling behavior,dynamic characteristics,evolution rules and optimization strategies among competitors,so as to provide theoretical basis for the optimization and decision-making among competitors in the actual project.At present,a lot of achievements have been accumulated in the research of competitor model,which gradually forms a theoretical framework with chaos,bifurcation and stability analysis as theoretical tools,partial differential equation and difference equation as the system structure.However,the existing research relies on the initial state given by the system.Because the competition game model has the initial value sensitivity,the initial state is the key to affect the evolution law of each competitor,and different initial value selection will lead to a different "evolution"process.Therefore,it is necessary to make effective supplementary research on the initial state of the evolution law of competitors by means of new theoretical tools.As an important branch of nonlinear dynamics,many fields of fractal theory study the initial set of the system trajectory stability and boundedness.Therefore,this paper takes fractal as the theoretical tool,and takes discrete two-dimensional and three-dimensional difference equation model as the research object,studies the dynamic properties,optimal control and application of the initial distribution fractal set of competitors.The details are as follows:firstly,the topological change law of the classical two-dimensional logistic competition model under the interference of external noise is studied,and the topological change law of the stable coexistence parameter set of competitors is studied to advance the research of one-step control optimization lays the theoretical foundation.Secondly,a class of three competitor models are studied,and the concept of Julia set is given to ensure the stable coexistence of competitors.By setting gradient control term,the competition process is disturbed to realize the control and optimization of the initial fractal set.Finally,the boundedness of a class of Julia sets of a single oligarch chain coupled competition model is proved;finally,the fractal dynamics analysis of the competition model is applied in the multi-channel supply chain price model,the boundary control of Julia set in the stable region is realized by means of optimizing the control method,so as to ensure the stability of market price.Through this study,the purpose of this paper is to supplement the dynamic research of competition game model from the perspective of fractal theory,and provide effective theoretical support for the relevant application research in economic and financial fields.