基于混合型泛函微分方程的Kaldor-Kalecki模型  

Kaldor-Kalecki model based on functional differential equation of mixed type

作　　者：刘澄[1] 刘祥东[1] 孙彬[1] 

机构地区：[1]北京科技大学东凌经济管理学院,北京100083

出　　处：《系统工程学报》2011年第6期738-745,共8页Journal of Systems Engineering

基　　金：国家社科基金重大资助项目(10ZD&029);北京科技大学博士研究生科研基金资助项目(06106061)

摘　　要：通过引入受预期资本存量影响的投资函数,将具有时滞的Kaldor-Kalecki商业周期模型拓展为混合型泛函微分方程系统.利用投资中的时滞或资本存量的预测时间作为分支参数,讨论均衡点的稳定性以及由Hopf分支形成商业周期的条件,并用数值模拟来验证所得结论.数值模拟结果显示:在较短的资本存量预测时间和投资时滞的影响下,生产总值和预期资本存量逐步趋向均衡,经济运行平稳;在较长的资本存量预测时间和投资时滞的影响下,生产总值和预期资本存量产生周期性振荡,商业周期出现.Through introducing investment function impacted by anticipated capital stock, a delayed Kaldor- Kalecki business cycle model is extended into a functional differential equation system of mixed type. By using delay in the investment or prediction time of capital stock as bifurcation parameter, this paper investigates the stability of equilibrium and the conditions of business cycle caused by Hopf bifurcation, and also provides numerical simulations to confirm the conclusions obtained. The results of numerical simulation indicate that affected by shorter prediction time of capital stock and shorter investment delay, the gross product and antic- ipated capital stock gradually tend to equilibrium, and economy steadily develops; while due to the influence of longer prediction time of capital stock and longer investment delay, the gross product and the anticipated capital stock generates cyclical oscillation, and business cycle appears.

关 键 词：Kaldor-Kalecki商业周期模型 预期资本存量 稳定性 HOPF分支 

分 类 号：F019.2[经济管理—政治经济学] O175.7[理学—数学]