Stability analysis of a business cycle model including anticipation and delay

A business cycle model with anticipation and delay was constructed by introducing anticipated capital stock into the investment decision function in the present period and considering investment delay in the capital accumulation process. This system's stability was investigated by using related theories of differential dynamical systems first. Then investment delay or the prediction time of capital stock was taken as a bifurcation parameter, and the conditions of Hopf bifurcation caused by the parameter were discussed. Last, some numerical simulations were carried out to confirm the obtained conclusions. It is shown that capital stock anticipation and investment delay together constitute the induced factors of business cycle. Economic fluctuations caused by investment delay can be dampened to some extend if the government makes investment decision based on short-term reasonable forecast on capital stock.