A Dynamic Analysis of the Business Cycle Model with a Fixed-time Delay

Abstract

In business activities, there is a certain time lag effect in investment and capital stock, which would affect the dynamic behavior of the business cycle model and then complicate the economic stability adjustment made through investment policies. Considering the influence on investment activities caused by the expectation time about capital stock, this paper, employing the Hopf bifurcation theory, with the delay in investment as the bifurcation parameter, not only studies the equilibrium stability of the business cycle model with a fixed-time delay, but also discusses the formation conditions of the business cycle. The research discovers that the investment lag during the investing process and the expectation time about the capital stock are two crucial incentives of the business cycle; meanwhile, the expecting equilibrium target can be met through the adjustment of the government investment policies. These findings may serve as guidelines in stabilizing the business cycle and making relative economic policies. The conclusion is verified through numerical simulation.

Keywords

• business cycle model
• fixed-time delay
• Hopf bifurcation theory
• stability
• numerical simulation