Dynamical Analysis And Control Of Two New Fractional Order Chaotic Systems

In recent years,the development of fractional calculus,the study of fractional system has attracted more and more attention of scholars at home and abroad,and has been widely used in many fields,such as biomedicine,economy and finance,applied mathematics etc.Compared with the integer system,the fractional system can not only reveal its historical memory and genetic properties,but also reflect the intrinsic characteristics of the system more accurately.In this paper,we study the dynamical properties and chaos control of fractional difference system and delay differential system.One is that establishing a fractional difference game model of three-dimensional supply chain which close to the actual situation by the theory of fractional difference based on supply chain game model.Another is establishing a new class of fractional delay financial model by adding an additional state variable based on fractional delay financial model.By using the theory of nonlinear dynamics,the dynamical characteristics are analyzed and the chaotic behaviors are controlled.The main researches are as follows:Firstly,the research background and significance of the two models are introduced,and the research status in China and abroad is summarized.Secondly,the related theory are given in this paper,including the numerical solution of fractional differential and difference equations,discrimination method of chaos,which lays the mathematics foundation for the study of fractional chaotic systems.Thirdly,a new class of three-dimensional supply chain fractional difference game model is constructed by using the theory of fractional difference.Then the numerical experiments are performed to analyze the complex dynamic behavior of the model,and the effect of the output adjustment speed parameter on the dynamical behaviors of the system is discussed.By using the method of parameter control,the double period bifurcation and unstable periodic orbit of the production of producers are controlled,which can make the model of chaos into the Nash equilibrium state again.Finally,a new class of fractional delay financial model is constructed,and the basic dynamical behaviors of the system are analyzed in detail.Furthermore,the stability of the system is analyzed by using the Lyapunov stability theory.And then the controller is designed to realize the chaos control of the system,which can provide the theoretical guidance for the stable development of the financial market.