Stability and Hopf bifurcation for a business cycle model with expectation and delay

作者：Liu, Xiangdong^*; Cai, Wenli; Lu, Jiajun; Wang, Yangyang

来源：Communications in Nonlinear Science & Numerical Simulation, 2015, 25(1-3): 149-161.

DOI：10.1016/j.cnsns.2015.02.003

• Hopf bifurcation
• Stability
• Direction
• Expectation
• Delay
• Business cycle

According to rational expectation hypothesis, the government will take into account the future capital stock in the process of investment decision. By introducing anticipated capital stock into an economic model with investment delay, we construct a mixed functional differential system including delay and advanced variables. The system is converted to the one containing only delay by variable substitution. The equilibrium point of the system is obtained and its dynamical characteristics such as stability, Hopf bifurcation and its stability and direction are investigated by using the related theories of nonlinear dynamics. We carry out some numerical simulations to confirm these theoretical conclusions. The results indicate that both capital stock's anticipation and investment lag are the certain factors leading to the occurrence of cyclical fluctuations in the macroeconomic system. Moreover, the level of economic fluctuation can be dampened to some extent if investment decisions are made by the reasonable short-term forecast on capital stock.

• 出版日期2015-8
• 单位中国矿业大学（北京）; 北京科技大学