一类时滞Solow模型的动态周期波动分析

李佼瑞; 张艳霞

doi:10.21656/1000-0887.380184

一类时滞Solow模型的动态周期波动分析

doi: 10.21656/1000-0887.380184

西安财经学院西安统计研究院, 西安 710100

基金项目: 国家自然科学基金（11572231）; 陕西省教育厅专项科研计划项目（16JK1301）

详细信息

作者简介:
李佼瑞（1973—），男，教授，博士（通讯作者. E-mail: jiaoruili@xaufe.edu.cn）;张艳霞（1988—），女，硕士生（E-mail: zhangyanxia1314@126.com）.

中图分类号: O211.63
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- 被引次数: 0
出版历程
- 收稿日期: 2017-06-28
- 修回日期: 2018-01-04
- 刊出日期: 2018-03-15

Dynamic Cycle Analysis of a Solow Model With Time Delays

Xi’an Statistical Research Institute, Xi’an University of Finance and Economics, Xi’an 710100, P.R.China

Funds: The National Natural Science Foundation of China（11572231）

摘要

摘要: 考虑到资本生产投资和污染治理投资的时滞性，为分析其对经济环境系统动态演化的影响机理，基于经典的Solow模型，引入环境净化和两个投资时滞参数.首次提出了带有环境净化的双时滞Solow模型，并分析了该模型的动态周期波动行为.结果表明：无论单个投资时滞还是两个投资时滞，均能诱发经济周期的产生；时滞越大，经济周期波动越强烈；通过调整投资决策可达到预期均衡目标，实现经济环境系统的周期稳定运行.
- Solow模型 /
- 时滞 /
- 经济周期 /
- Hopf分岔 /
- 极限环
Abstract: Based on the classical Solow model, a dual delay Solow model was proposed for the first time in view of the capital production investment time delay, the pollution treatment investment time delay and the environment purification parameters, to analyze the dynamic evolution mechanism of the economyenvironment system. Then the dynamic periodic fluctuation behavior of the model was discussed. The results show that the economic cycle will be triggered by any individual investment time delay or both 2 delays; with the increasing of the time delay, the economic cyclic fluctuation will become more intense; the appropriate adjustment of the investment policy will help achieve the expected equilibrium objective, and the stable cyclic operation of the economyenvironment system can be realized.
- Solow model /
- time delay /
- economic cycle /
- Hopf bifurcation /
- limit cycle

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参考文献(17)

[1]	KARRAS G. Land and population growth in the Solow growth model: some empirical evidence[J].Economics Letters,2010,109(2): 66-68.
[2]	GUERRINI L. The Solow-Swan model with a bounded population growth rate[J]. Journal of Mathematical Economics,2006,42(1): 14-21.
[3]	STAMOVA I M, STAMOV A G. Impulsive control on the asymptotic stability of the solutions of a Solow model with endogenous labor growth[J]. Journal of the Franklin Institute,2012,349(8): 2707-2716.
[4]	熊俊. 经济增长因素分析模型: 对索洛模型的一个扩展[J]. 数量经济技术经济研究, 2005,22(8): 25-34.(XIONG Jun. Analytical model of economic growth factors: an expansion of Solow model[J]. The Journal of Quantitative & Technical Economics,2005,22(8): 25-34.(in Chinese))
[5]	BROCK W A, TAYLOR M S. The Green Solow model[J]. Journal of Economic Growth,2010,15(2): 127-153.
[6]	魏立桥, 赵晓娜, 景文宏. 基于环境污染的经济增长模型——以广东省为例[J]. 软科学, 2008,22(2): 54-56.(WEI Liqiao, ZHAO Xiaona, JING Wenhong. Economic growth model based on environmental pollution—taking Guangdong province as an example[J]. Soft Science,2008,22(2): 54-56.(in Chinese))
[7]	ANTOCI A, RUSSU P, SORDI S, et al. Industrialization and environmental externalities in a Solow-type model[J]. Journal of Economic Dynamics and Control,2014,47(6): 211-224.
[8]	CELLINI R. Implications of Solow’s growth model in the presence of a stochastic steady state[J]. Journal of Macroeconomics,1997,19(1): 135-153.
[9]	LEI Dongxia, HUANG Yongzhong. Stationary distribution of stochastic Solow model[J]. Mathematica Application,2014,27(4): 775-778.
[10]	李佼瑞, 张艳霞. 带有环境净化的双随机参数Solow模型的稳定性[J]. 统计与信息论坛, 2016,31(6): 7-13.(LI Jiaorui, ZHANG Yanxia. The stability of the Solow model with double random parameters based on environmental purification[J]. Statistics and Information Forum,2016,31(6): 7-13.(in Chinese))
[11]	毕志伟, 胡适耕, 梅正阳. 一个时滞经济增长模型的动态分析[J]. 华中科技大学学报, 2001,29(9): 109-111.(BI Zhiwei, HU Shigeng, MEI Zhengyang. Dynamical analysis on the model for economic growth with delay[J]. Journal of Huazhong University of Science and Technology,2001,29(9): 109-111.(in Chinese))
[12]	YU Y, HAN X, ZHANG C, et al. Mixed-mode oscillations in a nonlinear time delay oscillator with time varying parameters[J]. Communications in Nonlinear Science and Numerical Simulation,2017,47: 23-34.
[13]	WU X P. Zero-Hopf bifurcation analysis of a Kaldor-Kalecki model of business cycle with delay[J]. Nonlinear Analysis: Real World Applications,2012,13(2): 736-754.
[14]	LIU C, LU N, ZHANG Q. Dynamical analysis in a hybrid bioeconomic system with multiple time delays and strong Allee effect[J]. Mathematics and Computers in Simulation,2017,136: 104-131.
[15]	王万永, 陈丽娟. 具有时滞耦合的n个Van der Pol振子弱共振双Hopf分岔[J]. 应用数学和力学, 2013,34(7): 764-770.(WANG Wanyong, CHEN Lijuan. Weak resonant double Hopf bifurcation of n Van del Pol oscillators with delay coupling[J]. Applied Mathematics and Mechanics,2013,34(7):764-770.(in Chinese))
[16]	PASCHE M. Technical progress, structural change and the environmental Kuznets curve[J]. Ecological Economics,2002,42(3): 381-389.
[17]	陈六君, 毛潭, 刘为, 等. 环境恶化与经济衰退的动力学模型[J]. 北京师范大学学报(自然科学版), 2004,40(5): 617-622.(CHEN Liujun, MAO Tan, LIU wei, et al. A dynamic model on environmental degradation and economic recession[J]. Journal of Beijing Normal University(Natural Science),2004,40(5): 617-622.(in Chinese))