Complex Dynamics Study Of Some Particular Inventory Management Chaotic Model

This article studies the complex dynamics properties of some specific inventorymanagement chaotic model in the economic system. It first establishes an inventorymanagement chaos model with inventory capital transfer rates p=0, and then introducesthe general inventory management chaotic model. Utilizing the discrete-time dynamicsystem theory, it gets the stability of the fixed points in the model when p=0, giving thecorresponding parameter conditions of it. And strictly prove that there is a Neimark-Sackerbifurcation on the fixed point and get the approximate expression of the invariant cycleproduced by the Neimark-Sacker bifurcation then showing it by Matlab. In addition, thispaper utilizes the Jacobi algorithm to calculated the Lyapunov exponent spectrum of thesystem, and conclude that there is chaos in the system by numerical simulation. At thesame time, for the general inventory management chaotic model, we use theory analysisstrictly proving the existence and the stability of the fixed point. Besides, by the numericalsimulation, we find that there is a Neimark-Sacker bifurcation on the fixed point and itoccurs an invariant cycle. After that we find the existence of chaos in the system based onits Lyapunov exponent and the0-1test. At last combining with the practical significance ofthe model, it reveals the model’s economic nature which is related to chaos is determinedby its nonlinearity, and provies certain information for making corresponding economiccountermeasures.The main contents of this paper are as follows.The first chapter introduces the background, significance of the research and themajor works. It outlines a brief review of research and development history of the dynamicsystem, as well as its bifurcation and chaos’s. Then it recalls the basic concepts of thedynamic system, the local bifurcation theory, as well as the concept and determinationmethods of chaos. On the other hand, it gives a short introduce of the utilization ofdiscrete-time system dynamics in the economic and the research status of inventorymanagement model.The second chapter gives the inventory management chaotic model. According toinventory management principle in the supply chain management, we first put out aninventory management model with inventory capital transfer rates p=0, which bases onsales base, product resources rate, inventory efficient under the action of volume and aboutcustomers and inventory quantity. Moreover we put out the general inventory managementchaotic model based on sales base, stock capital transfer rate, product resources rate, inventory efficient and about sales resource, customers and inventory quantity.The third chapter detects the local dynamics analysis and chaos existence of theinventory management chaotic model when the inventory capital transfer rate p=0. Byanalyzing the stability of the fixed point, it obtains the deciding condition of the stabilityand the non-existence of the Fold bifurcation and Flip bifurcation. Moreover, it strictlyproves the existence of the Neimark-Sacker bifurcation and gains the approximateexpression of the invariant cycle produced by the Neimark-Sacker bifurcation thenvalidates it by numerical simulation. At the same time, it gives the Lyapunov exponentspectrum of the system utilizing the Jacobi algorithm, and then shows the chaos’ existencenumerically.The fourth chapter discusses the local dynamics analysis and chaos existence of thegeneral inventory management chaos model. It strictly proves the existence and thestability of the fixed point. By the numerical analysis, it can see that, when the fixed pointloses stability, a Neimark-Sacker bifurcation would occurs. In addition, Lyapunovexponent and0-1chaos test are utilized to find out the existence of chaos.