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首页> 外文期刊>Nonlinear dynamics, psychology and life sciences >Numerical Exploration of Kaldorian Interregional Macrodynamics: Stability and the Trade Threshold for Business Cycles Under Fixed Exchange Rates
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Numerical Exploration of Kaldorian Interregional Macrodynamics: Stability and the Trade Threshold for Business Cycles Under Fixed Exchange Rates

机译：Kaldorian区域间宏观动力学的数值探索：固定汇率下商业周期的稳定性和贸易阈值

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摘要

The stability of equilibrium and the possibility of generation of business cycles in a discrete interregional Kaldorian macrodynamic model with fixed exchange rates are explored using numerical methods. One of the aims is to illustrate the feasibility and effectiveness of the numerical approach for dynamical systems of moderately high dimensionality and several parameters. The model considered is five-dimensional with four parameters, the speeds of adjustment of the goods markets and the degrees of economic interactions between the regions through trade and capital movement. Using a grid search method for the determination of the region of stability of equilibrium in two-dimensional parameter subspaces, and coefficient criteria for the flip bifurcation - and Hopf bifurcation - curve, we determine the stability region in several parameter ranges and identify Hopf bifurcation curves when they exist. It is found that interregional cycles emerge only for sufficient interregional trade. The relevant threshold is predicted by the model at 14 - 16 % of trade transactions. By contrast, no minimum level of capital mobility exists in a global sense as a requirement for the emergence of interregional cycles; the main conclusion being, therefore, that cycles may occur for very low levels of capital mobility if trade is sufficient. Examples of bifurcation and Lyapunov exponent diagrams illustrating the occurrence of cycles or period doubling, and examples of the development of the occurring cycles, are given. Both supercritical and subcritical bifurcations are found to occur, the latter type indicating coexistence of a point and a cyclical attractor.
机译：使用数值方法探索了具有固定汇率的离散区域间卡尔多里亚宏观动力学模型中均衡的稳定性和商业周期产生的可能性。目的之一是说明数值方法对于中等高维数参数的动力学系统的可行性和有效性。所考虑的模型是具有四个参数的五维模型，货物市场的调整速度以及区域之间通过贸易和资本流动的经济互动程度。使用网格搜索方法确定二维参数子空间中平衡的稳定性区域，并确定翻转分叉-和Hopf分叉-曲线的系数准则，我们确定几个参数范围内的稳定性区域，并确定Hopf分叉曲线当它们存在时。已经发现，区域间周期仅在足够的区域间贸易中出现。该模型预测了相关阈值，占贸易交易的14-16％。相比之下，就区域间周期的出现而言，在全球范围内不存在最低限度的资本流动性。因此，主要结论是，如果贸易充足，那么对于极低水平的资本流动性可能会出现周期。给出了分叉和Lyapunov指数图的示例，这些示例说明了周期或周期加倍的发生，并给出了发生周期的发展示例。发现超临界和亚临界分叉都发生，后一种分叉表明一个点和一个循环吸引子并存。

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