考虑记忆性质与时间滞后效应的非线性经济周期模型分析

Analysis of the Nonlinear Business Cycle Model with Memory Property and Time Delay

考虑非线性经济周期模型中经济变量存在记忆性质与时间滞后现象,研究随机周期作用激励下Goodwin模型的随机响应,以此研究记忆性质与时间滞后现象对经济周期波动的具体影响。通过随机多尺度方法得到了模型的确定性与随机情形下的稳态响应。结果发现:当考虑非线性投资函数时,经济变量的时间记忆性质和时间滞后现象均可以导致经济波动方式的改变;当考虑非线性消费函数时,经济变量的时间记忆性质与时间滞后现象均可以诱导出经济周期波动的随机跳跃现象,即引发经济系统的突变。同时,随机周期作用也可以诱发系统出现稳态概率密度函数的分岔现象出现,说明外部随机周期作用可以诱发经济系统的突变现象产生。

In this paper,multi-scales method is applied to obtain the primary resonance response of the business cycle model with fractional delay under the narrowband random excitation.The steady-state responses in deterministic and stochastic cases are studied.The validity of the method is verified by the simulation solutions.By analyzing two examples,the effect of the fractional derivative on the amplitude of the system and the stationary probability function is investigated.When the consumption function is nonlinear function,the change of the fractional derivative and time delay can both induce the stochastic jump.Also,the intensity of the random excitation can induce the P-bifurcation of the stationary probability function.