Bifurcation Analysis On The Economic Dynamics Model With Time-delay

For a long time, people pay more an attention to economic problems. Economicproblems are not only closely related to everyone’s daily life, also has a relationshipwith social development, national stability. Because of the economy in the processof operation is complex and instable, the external conditions change a little cancause the instability of the whole economy system. There are many factors that canlead the system instability, such as market adjustment coefficient, the degree ofcapital flows and so on. Therefore, when people grasp the factors that influence theeconomic fluctuation, we will take effective measures to adapt economicfluctuations of the market and provide the theoretical basis to predict the economicdevelopment.Due to the gross domestic product is influenced by the past investment decision.Therefore, this article will extend Kaldorian model to Kaldorian model with timedelay, and study the dynamic property of this model. This paper uses thecharacteristic value method, Routh-Hurwotz criterion, normal form method andcenter manifold theory to analyze Kaldorian business cycle model. Through theanalysis of system characteristic equation, using the Routh-Hurwotz criterion to getthe stable conditions of the system equilibrium, through the analysis of thedistribution of eigenvalues and validation of transversality condition, we will get thecritical value of hopf bifurcation, and using the center manifold thesis to analyze thebifurcation direction and the stability of periodic solutions.