| 具双时滞的Kaldor-Kalecki系统的Hopf分支 |
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| 引用本文： | 徐秀艳,朱捷,王佳秋.具双时滞的Kaldor-Kalecki系统的Hopf分支[J].哈尔滨商业大学学报(自然科学版),2012,28(4):472-476. |
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| 作者姓名： | 徐秀艳 朱捷 王佳秋 |
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| 作者单位： | 黑龙江科技学院理学院,哈尔滨,150027 |
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| 基金项目： | 黑龙江科技学院引进人才科研启动基金项目(06-138) |
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| 摘 要： | 讨论了具双时滞的Kaldor-Kalecki商业周期系统的稳定性.以时滞、调节系数为参数,通过对系统线性化方程的特征根的分布分析,得到系统平衡点的稳定性条件,确定了系统平衡点的线性稳定性区域.讨论了系统Hopf分支的存在条件,利用中心流形理论和规范型方法计算了系统Hopf分支方向和分支周期解的稳定性.应用Matlab软件进行了数值模拟,其结果与理论分析结果一致.
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| 关 键 词： | 商业周期 时滞 Hopf分支 规范型 |
Hopf bifurcation analysis in Kaldor-Kalecki model of business cycle with two time delays |
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| XU Xiu-yan
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ZHU Jie
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WANG Jia-qiu.Hopf bifurcation analysis in Kaldor-Kalecki model of business cycle with two time delays[J].Journal of Harbin University of Commerce :Natural Sciences Edition,2012,28(4):472-476. |
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| Authors: | XU Xiu-yan ZHU Jie WANG Jia-qiu |
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| Institution: | (School of Science,Heilongjiang Institute of Science and Technology,Harbin 150027,China) |
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| Abstract: | This paper investigated a Kaldor-Kalecki model of business cycle system with two time delays.The linear stability of the model was carried out.The time delayand the adjustment coefficientwere taken as parameters,the condition to ensure the stability of the zero solution and its stable domain were decided by analyzing the characteristic equation of the linearization.The existence of Hopf bifurcation was given.Discussed the direction and stability of the Hopf bifurcation by using the center manifold theory and normal form method.Some numerical simulations by using Matlab software supported the theoretical results. |
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| Keywords: | business cycle time delay Hopf bifurcation normal form |
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