Study of Economic Fluctuations Using the Method of Nonlinear Dynamics

用非线性动力学方法研究经济波动

• 批准号: 11630020
• 负责人: INABA Toshio
• 金额: $ 1.54万
• 依托单位: Waseda University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11630020/
• 关键词: Business Cycle; Nonlinear Dynamics; Chaos; Noise; 経済変動; 非線形差分方程式; 微分-差分方程式; 持続可能性; マクロ動学モデル

(1) One Dimensional ModelsChaos occurs in a nonlinear cobweb model with normal demand and supply, naive expectations and adaptive production adjustment. We demonstrates the possibility that chaotic fluctuations may be preferable to a steady state for a simple macro disequilibrium model in which inventory can be chaotically fluctuated.(2) High Dimensional ModelsWe investigate the global dynamics of two-dimensional Diamond-type overlapping generations model extended to allow for government intervention. We identify conditions under which transverse homoclinic points to the golden rule steady state are generated. We examine by mean of analytical method and numerical simulations the properties of three-dimensional Kaldor-type business cycle models in which a parameter is fluctuated by noise. It is shown that noise may not obscure the underling structures, but also reveal the hidden structures.(3) New Numerical Approximation SchemesComposition methods for autonomous stochastic differential equations (SDEs) are formulated to produce numerical approximation schemes for the equations. The new schemes are advantageous to preserve the special character of SDEs numerically and are useful for approximations of the solutions to stochastic nonlinear equations(4) Alternative Approaches and ModelsWe investigate various alternative approaches and models. For example, percolation theory is employed to model stock price fluctuations.

(1)一维模型混沌发生在具有正常需求和供给、幼稚预期和适应性生产调整的非线性蛛网模型中。我们证明了对于库存可能发生混沌波动的简单宏观不平衡模型来说，混沌波动可能比稳态更可取。（2）高维模型我们研究了二维钻石型重叠世代模型的全局动态，并扩展到允许政府干预。我们确定了生成黄金法则稳态的横向同宿点的条件。我们通过分析方法和数值模拟研究了参数受噪声波动的三维卡尔多型经济周期模型的性质。结果表明，噪声可能不会掩盖底层结构，而且还会揭示隐藏的结构。(3)新的数值逼近方案制定了自主随机微分方程(SDE)的组合方法，以产生方程的数值逼近方案。新方案有利于在数值上保留 SDE 的特殊性，并且对于随机非线性方程解的近似很有用。(4) 替代方法和模型我们研究了各种替代方法和模型。例如，采用渗流理论来模拟股票价格波动。

项目成果

T.Misawa: "Numerical Integration of Stochastic Differential Equations by Composition Methods"京都大学数理解析研究所講究録. 1180. 166-190 (2000)

T. Misawa：“通过组合方法进行随机微分方程的数值积分”京都大学数学科学研究所 Kokyuroku。1180. 166-190 (2000)

稲葉敏夫, 浅田統一郎, 三沢哲也: "Nonlinear Macroeconomic Dynamics : A Study of Noise Effects"電子情報通信学会・信学技報. NLP2001-64. 79-88 (2001)

Toshio Inaba、Tochiro Asada、Tetsuya Misawa：“非线性宏观经济动力学：噪声影响研究”IEICE/IEICE 技术报告。 79-88 (2001)。

H.Tanaka: "Iterated Elimination and No Tracle Theorem"京都大学数理解析研究所講究録. 1215. 182-194 (2001)

H. Tanaka：“迭代消除和无踪定理”京都大学数学科学研究所 Kokyuroku。1215. 182-194 (2001)

T. Onozaki, G. Sieg and M. Yokoo: "Complex Dynamics in a Cobweb Model with Adaptive Production Adjustment"Journal of Economic Behavior and Organization 41. 101-115 (2000)

T. Onozaki、G. Sieg 和 M. Yokoo：“具有自适应生产调整的蛛网模型中的复杂动态”经济行为与组织杂志 41. 101-115 (2000)

T.Onozaki, G.Sieg, M.Yokoo: "Complex Dynamics in a Cobweb Model with Adaptive Production Adjustment"Journal of Economic Behavior and organization. 41. 101-115 (2000)

T.Onozaki、G.Sieg、M.Yokoo：“具有自适应生产调整的蛛网模型中的复杂动态”经济行为与组织杂志。