含有预期和时滞的经济周期模型稳定性分析

将预期的资本存量引入现阶段的投资决策函数，同时考虑资本积累过程中的投资时滞，构建一个含有预期和时滞的经济周期模型.首先利用微分动力系统相关的理论研究系统的稳定性，然后把投资时滞或资本存量的预测时间作为分支参数，讨论由此参数导致Hopf分支的条件，并执行一些数值模拟以验证所得结论.研究结果表明:资本存量预期和投资时滞共同构成经济周期的诱导因素；对资本存量进行短期合理的预测，据此制定投资决策，能够在一定程度上冲销由投资时滞所造成的经济波动. 

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.