Complex and Chaotic Nonlinear Dynamics
Complex and Chaotic Nonlinear Dynamics
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复杂混沌非线性动力学
DOI：
10.1007/978-3-540-85978-9
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Vialar. Thierry
中科院分区：
文献类型：
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作者：
Vialar. Thierry
自20世纪70年代以来，复杂和混沌非线性动力学（简而言之，复杂动力学）构成了一个日益增长和日益重要的领域，包括先进的研究活动和强烈的跨学科方法。这个领域是包括经济学在内的许多科学的基本兴趣所在。让我们先评论一下《经济学中的复杂动力学》的兴趣，以及这样一本书的必要性和它的跨学科性：《经济学中的数学》具有很强的教学作用。数学表明理论模型和范例必须符合测量。然而，在经济学中，这种测量是罕见的，除了股票市场之外，更多的是少量的点和非常低的密度。这种将经济学与“密集的”可测量的现实分离开来的鸿沟使经济学家处于一种“孤立”状态（与其他科学相比）：(1)定性方法可以进行，例如，以文学的方式进行，通常具有很大的相关性，但不是定量的；(2)模型的构建（“数学理想”）具有强烈的说教或机械的使命，通常远离“生活”的丰富性。这首先是一个测量问题。除了非线性理论的认识论革命之外，今天还有信息系统和网络的革命，这将为在经济学的许多领域（例如从消费者行为到国民账户）捕获密集的测量提供难得的机会。因此，经济学家将处于与以前相反的境地。经济学家的计量流的密度将越来越接近于其他科学的计量流，例如，这些科学的计量流来自“活人”。经济学必须用相关工具来处理这些度量流，而掌握这些工具是必要的。这是经济学的一个转折点。因此，数学及其分析工具对经济学家来说比以往任何时候都更有意义，特别是在研究复杂动力学和带来更接近的理论模型和来自信号或时间序列测量的信息时。计算能力、网络、测量和信息处理也使这样一本书的存在变得合法和必要。
Since the 1970s, Complex and chaotic nonlinear dynamics (in short, Complex Dynamics) constitute a growing and increasingly important area that comprises advanced research activities and strongly interdisciplinary approaches. This area is of a fundamental interest in many sciences, including Economics. Let us start with a comment about the interest of Complex Dynamics in Economics and in so doing the necessity of such a book and its interdisciplinarity: Mathematics in Economics have a very strong didactic role. Mathematics state theoretical models and paradigms that must conform to measurements. However, in Economics the measurements are rare, more often of a small number of points and of a very low density, except for stock markets. This chasm that separates Economics from the “dense” measurable reality has maintained economists in a kind of “isolation”(compared with other sciences):(1) that of the qualitative approach that can be conducted, for instance, in a literary way, very often of great relevance but which is not quantitative,(2) and that of the construction of models (“mathematical idealities”) with a strong didactic or mechanistic vocation often far from the richness of “the living”. This is above all a problem of measurement. Beyond the epistemological revolution of nonlinear theory, today there is that of the information systems and networks, which will provide the exceptional opportunity to capture dense measurements in numerous fields of Economics (eg from consumer behaviors up to national accounts). Thus, the economists will be in an opposite situation than before. The measure flows for the economists will have densities increasingly similar to those of other sciences whose measures come from “the living” for example. Economics will have to treat these measure flows with relevant tools, which are necessary to master. This is a turning point for Economics. Thus, Mathematics and its analytic tools are more relevant than ever for economists, in particular to study Complex Dynamics and to bring closer theoretical models and information coming from signal or time series measurements. Calculation capabilities, networks, measurements and information treatment also make the existence of such a book legitimate and necessary.