Analysis Of Competition In The Market Structure With Time Delay Under The Theory Of Biological Populations

Based on the similarity of market and population competition process, the biological population theories are creatively applied to analyze the market competition process. According to the different market structure, the completely competitive market model, oligarchic market model, monopolistic competition market model and the monopoly market model with time delay are established. By using the method of time delay system research in biological population theories, the evolution process of perfectly competitive market, oligarchs market, monopolistic competition market and monopoly market with time delay are integrally researched; the conclusions which we get are very useful for the production and operation of enterprises and government management decisions.Firstly, three manufacturers of competition model with consumptive and competitive time delay are established, through analyzing the characteristic equation at the positive equilibrium, and then the conditions of emerging hopf bifurcations are presented. On that basis, by means of the normal form method and center manifold theorem, the direction and stability of hopf bifurcations are discussed. Conditions for Continuous coexistence of three manufacturers are presented, and then the stable equilibrium of three competing firms are influenced by time delay. The numerical simulation applying matlab is demonstrated.Furthermore, the numbers of manufacturers which participate in market competition process are extended. The competitive models with consumptive and competitive time delay of n firms are set up. By using a clever method that the characteristic equations is decomposed into factor multiplication, the characteristic equations in positive equilibrium is analyzed, then the create conditions of hopf bifurcations are showed. In particular, to monopoly market types when N=1, the diffusion model with delays of the single manufacturer are built. To the oligarchs market types with N=2, the competitive model with consumptive and competitive time delay are built. Through analyzing the characteristic equations of the both models, the conditions of the Hopf bifurcations are presented. Conditions for Continuous coexistence of manufacturers are presented, and then the stable equilibrium of competing firms are influenced by time delay. In addition, the numerical simulation is given.Finally, explain the corresponding economics significance of hopf bifurcations which is competing firms can coexist with the form of cycle concussion in some scope. In addition, some Suggestions on how to eliminate the time delay are given. At last, some problems are prospected, such as the dynamic evolution process which classical economics theory are not involved, and eliminate delay using impulsive control method, etc.