Stochastic Analysis of a Nonlinear Business Cycle Model with Correlated Random Income Disturbance

The economic cycle has always been an important feature of the evolution of an economic system. In the presence of many uncertain factors, it appears in the manner of very complex nonlinearity and randomness. Based on the theory of stochastic nonlinear dynamics, a nonlinear economic cycle model with correlated random income disturbance is established. The probability density evolution of the nonlinear economic cycle model under random disturbance is numerically analyzed by using a path integration method. The analysis shows the high saving rate reduces the investment and improves the probabilities of low income and low income change rate. In order to achieve a higher income, the saving rate should be controlled to some reasonable small value. The nonlinearity of the economic cycle model increases the probabilities of high income and high income change rate, which can lead to the increase of income in a probabilistic sense. The increase of random income interference enhances the uncertainty of income. Meanwhile, the increase of correlated random income disturbance can lead to a nonsymmetric distribution of the probability distributions of income and income change rate. In such cases, the income is more difficult to forecast and control.