| 具有时滞的Kaldor-Kalecki商业周期模型Hopf分支的频域分析 |
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| 引用本文： | 于晋臣,彭名书,张彩艳.具有时滞的Kaldor-Kalecki商业周期模型Hopf分支的频域分析[J].北方交通大学学报,2014(3):146-151. |
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| 作者姓名： | 于晋臣 彭名书 张彩艳 |
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| 作者单位： | [1]北京交通大学理学院,北京100044 [2]山东交通学院理学院,济南250357 [3]山东电子职业技术学院,济南250014 |
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| 基金项目： | 国家自然科学基金资助项目（10871019,61308018）;山东省高校科技计划资助项目（J12LI55）;山东交通学院院科研基金项目资助（Z201203,Z201030） |
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| 摘 要： | 研究了一类具有时滞的Kaldor-Kalecki商业周期模型.首先,将时滞作为分支参数,应用Nyquist准则分析了Hopf分支的存在性;然后,应用频域法和图示Hopf分支定理研究了Hopf分支的方向和周期解的稳定性;最后,对该模型进行了数值仿真,仿真结果验证了理论分析的正确性.
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| 关 键 词： | 时滞 频域 商业周期模型 图示Hopf分支定理 |
Frequency domain analysis for Hopf bifurcation of a Kaldor-Kalecki business cycle model with time delay |
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| YU Jinchen,PENG Mingshu,ZHANG Caiyan.Frequency domain analysis for Hopf bifurcation of a Kaldor-Kalecki business cycle model with time delay[J].Journal of Northern Jiaotong University,2014(3):146-151. |
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| Authors: | YU Jinchen PENG Mingshu ZHANG Caiyan |
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| Institution: | 1.School of Science, Beijing Jiaotong University, Beijing 100044, China;2.School of Science,Shandong Jiaotong University, Jinan 250357, China; 3.Shandong College of Electronic Techonlogy,Jinan 250014, China) |
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| Abstract: | This paper investigates a Kaldor-Kalecki model of business cycle system with time delay.Firstly,by using delay as bifurcation parameter and applying the Nyquist criterion,the authors discuss the existence of Hopf bifurcation.Then,the direction and the stability of Hopf bifurcation periodic solutions are determined by the frequency domain approach and the graphical Hopf bifurcation theorem.Finally,some numerical simulations for justifying the theoretical analysis are also provided. |
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| Keywords: | time delay frequency domain business cycle model graphical Hopf bifurcation theorem |
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