Stability and bifurcation analysis for the Kaldor–Kalecki model with a discrete delay and a distributed delay
Stability and bifurcation analysis for the Kaldor–Kalecki model with a discrete delay and a distributed delay
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DOI：
10.1016/j.physa.2016.04.041
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发表时间：
2016-10
影响因子：
3.3
通讯作者：
Jinchen Yu;Mingshu Peng
中科院分区：
文献类型：
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作者：
Jinchen Yu;Mingshu Peng
本文研究了一类具有离散时滞和分布时滞的Kaldor-Kalecki经济周期模型。通过分析相应的特征方程，研究了正平衡点的局部稳定性。当离散时滞通过一个临界值序列时，系统存在Hopf分支。应用多重尺度法，得到了确定系统Hopf分支方向和分支周期解稳定性的显式公式。最后，数值模拟来说明我们的主要结果。
In this paper, a Kaldor–Kalecki model of business cycle with both discrete and distributed delays is considered. With the corresponding characteristic equation analyzed, the local stability of the positive equilibrium is investigated. It is found that there exist Hopf bifurcations when the discrete time delay passes a sequence of critical values. By applying the method of multiple scales, the explicit formulae which determine the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Finally, numerical simulations are carried out to illustrate our main results.